ALBERT

Beschreibung: In many structures the final stress states are dependent on the sequence of construction or the stress states at various stages of construction are of interest. Such problems can be analyzed using finite element programs that have the capability of adding (birthing) elements to simulate the progress of construction. However, the usual procedure of assembling elements may lead to numerical instabilities or stress states that are unrealistic. Both problems are demonstrated in the analysis of a structure using the program ADINA. A technique which combines application of a preload with element birthing to overcome these problems is described and illustrated.

Beschreibung: A technique utilizing finite element analysis, liquid impact kinematics, and momentum theory is described and compared to single-drop impact test data performed on various configurations of coated ceramic material. The method correlates well with test data and is useful in predicting the single-drop impact damage velocity threshold for low-density, coated ceramic materials.

Beschreibung: An algorithm is outlined for simulating the contact surface erosion for impact problems. The algorithm dynamically relocates the contact surface as projectile and target materials exceed their failure criterion. Example computations of axisymmetric and oblique impacts are compared with experimental data.

Beschreibung: A study of the dynamic characteristics of a coupled translational-rotational system is given. The formulation of the problem considers the soil-structure interaction effects by utilizing the impedance functions at the foundation of a structure. Due to the fact that the coefficient matrix in the characteristic equation is frequency dependent in nature, iterations have to be performed to find the nature frequencies of the system. Examples and discussions are presented. Comparisons of the analytical results from various approaches are also given.

Beschreibung: Two analytical techniques applicable to large deflection dynamic response calculations for pressure loaded composite sandwich panels are demonstrated. One technique utilizes finite element modeling with a single equivalent layer representing the face sheets and core. The other technique utilizes the modal analysis computer code DEPROP which was recently modified to include transverse shear deformation in a core layer. The example problem consists of a simply supported rectangular sandwich panel. Included are comparisons of linear and nonlinear static response calculations, in addition to dynamic response calculations.

Beschreibung: The design of thin shell structures with respect to elastoplastic buckling requires an extended analysis of the influence of initial imperfections. For conservative design, the most critical defect should be assumed with the maximum allowable magnitude. This defect is closely related to the initial postbuckling behavior. An algorithm is given for the quasi-static analysis of the postbuckling behavior of structures that exhibit multiple buckling points. the algorithm based upon an energy criterion allows the computation of the critical perturbation which will be employed for the definition of the critical defect. For computational efficiency, the algorithm uses the reduced basis technique with automatic update of the modal basis. The method is applied to the axisymmetric buckling of cylindrical shells under axial compression, and conclusions are given for future research.

Beschreibung: A general approach is required for describing matter of behavior when the failure is likely to involve growth and coalescence of a large number of fractures. Failures of this kind appear frequently in rapid dynamic processes, particularly in the formation of spall fragments. An approach to formulating constitutive relations that accounts for the opening, shear and growth of an ensemble of cracks is discussed. The approach accounts for plastic flow accompanying fragmentation. The resulting constitutive relations were incorporated into a Lagrangian computer program. A theoretical approach to coalescence is described. The simplest formulation uses a linear Liouville equation, with crack growth limited by the mean free path of cracks, assumed constant. This approach allows for an anisotropic distribution of cracks. An alternative approach in which the decrease of the mean free path with increasing crack size is accounted for, but the crack distribution is assumed isotropic is described. A reduction of the governing Liouville equation to an ordinary differential equation of third order is possible, and the result can be used to determine how mean free path decreases with increasing crack size.

Beschreibung: The design of a composite panel requires some way of finding the minimum thickness laminate which will withstand the load requirements without failure. The mathematical complexity of this problem dictates the use of nonlinear optimization techniques. Specialized laminate optimization programs were developed which are compact and efficient enough to run on microcomputers. Only stresses at a point and inplane loads and deflections are considered. The programs are simple to use and require no knowledge of optimization. Techniques are developed which find minimum thickness laminates with either ply ratios or ply angles as design variables. A method is presented for finding the optimum orientation for the axis of symmetry of an orthotropic laminate. The orthotropic laminate program uses an approximate failure theory, which speed up computations dramatically.

Beschreibung: The evaluation of the total probability of a plastic collapse failure P sub f for a highly redundant structure of random interdependent plastic moments acted on by random interdepedent loads is a difficult and computationally very costly process. The evaluation of reasonable bounds to this probability requires the use of second moment algebra which involves man statistical parameters. A computer program which selects the best strategy for minimizing the interval between upper and lower bounds of P sub f is now in its final stage of development. The relative importance of various uncertainties involved in the computational process on the resulting bounds of P sub f, sensitivity is analyzed. Response sensitivities for both mode and system reliability of an ideal plastic portal frame are shown.

Beschreibung: A finite element modeling technique which utilizes a triangular element called TSHEL with 45 degrees of freedom and seven point integration was tested for analysis of thin plate and shell structures. The element formulation is based on the degenerate solid shell concept and the mixed formulation with assumed independent inplane and transverse shear strains. The effectiveness of the present modeling technique which features combined use of elements with kinematic modes and those without kinematic modes to eliminate both locking and spurious kinematic modes at the global structural levels are shown.

Beschreibung: The stress derivative technique for control of keystoning deformation in under-integrated finte elements is based on expansion of the stress in a Taylor series about the element center and retention of additional terms beyond the constant stress term. It has the advantage over other control techniques that keystoning resistance is provided by actual rather than artificial material properties. Application of this technique to the quadrilateral ring elements used for modelling solids of revolution subjected to axisymmetric loads is described. In a cylindrical coordinate system additional terms appear in the formulation which must be dealt with in arriving at a workable keystoning control scheme.

Beschreibung: An existing program is currently being adapted to perform finite element analysis by distributing substructures over a network of four Apple IIe microcomputers connected to a shared disk. In this network, one microcomputer controls the entire process while the others perform the analysis on each substructure in parallel. This substructure analysis is used in an iterative, fully stressed, structural resizing procedure. This procedure allows experimentatation with resizing in which all analyses are not completed during a single iteration. This research gives some insight on how to configure multidiscriplinary analysis and optimization procedures for decomposable engineering systems using either high performance engineering workstations or a parallel processor supercomputer. In addition, the operational experience gained facilitates the implementation of analysis programs on these new computers when they become available in an engineering environment.

Beschreibung: Described are the experiences gained from solving for the dynamic response of two simple structures on an experimental Multiple Instruction Multiple Data (MIMD) computer called the finite element machine. Introduced are MIMD computing concepts, describing how the concurrent algorithmic techniques implemented and giving results for the two example problems. The results show computational speedups of up to 7.83 using eight of the finite element machine processors and indicate that significant computational speedups are possible for large order structural computations.

Beschreibung: The FLEX/32 Multicomputer is a generic environment for cooperating multiple processors. The FLEX/32 supports a number of different processors, making it heterogeneous in terms of the instruction sets it supports, and homogeneous in its ability to provide consistent storage and input/output facilities to its differing processors. These facilities are accessed through standard 32-bit VMEbus connections. The FLEX/32 supports the full UNIX System V Operating System and languages associated with it, plus the extended ConCurrent C and Concurrent FORTRAN 77 languages that allow programming of concurrent software at a high level. Direct programming support at all levels is provided by the environment hardware for concurrent software execution and optimization, including hardware support for shared resource access arbitration, conditional critical region arbitration, and interprocessor messages.

Beschreibung: Research aimed at faster, more cost effective parallel machines and algorithms for improving designer productivity with finite element computations is discussed. A set of 8 boards, containing 4 nearest neighbor connected arrays of commercially available floating point chips and substantial memory, are inserted into a commercially available machine. One-tenth Mflop (64 bit operation) processors provide an 89% efficiency when solving the equations arising in a finite element problem for a single variable regular grid of size 40 by 40 by 40. This is approximately 15 to 20 times faster than a much more expensive machine such as a VAX 11/780 used in double precision. The efficiency falls off as faster or more processors are envisaged because communication times become dominant. A novel successive overrelaxation algorithm which uses cyclic reduction in order to permit data transfer and computation to overlap in time is proposed.

Beschreibung: The design, manufacture, and testing of an isolation system placed under a bench which simulates a space platform during testing in a hard vacuum are described. A low natural frequency isolation system is used to decouple ground vibrations from the bench. The materials used are vacuum compatible and do not introduce unwanted matter which would contaminate the payload optics and/or the testing environment. The system accommodates payloads of varying weights and envelopes.

Beschreibung: The potential cost and performance advantages of welding was understood but ignored by solar panel manufacturers in the U.S. Although NASA, DOD and COMSAT have supported welding development efforts, soldering remains the only U.S. space qualified method for interconnecting solar cells. The reason is that no U.S. satellite prime contractor found it necessary, due to mission requirements, to abandon the space proven soldering process. It appears that the proposed NASA space station program will provide an array requirement, a 10 year operation in a low Earth orbital environment, that mandates welding. The status of welding technology in the U.S. is assessed.

Beschreibung: Solid rocket booster cavity collapse flight measurements included external pressures on the motor case and aft skirt, internal motor case pressures, accelerometers located in the forward skirt, mid-body area, and aft skirt, as well as strain gages located on the skin of the motor case. This flight data yielded applied pressure longitudinal and circumferential distributions which compare well with model test predictions. The internal motor case ullage pressure, which is below atmospheric due to the rapid cooling of the hot internal gas, was more severe (lower) than anticipated due to the ullage gas being hotter than predicted. The structural dynamic response characteristics were as expected. Structural ring and wall damage are detailed and are considered to be attributable to the direct application of cavity collapse pressure combined with the structurally destabilizing, low internal motor case pressure.

Beschreibung: Researchers define damage-tolerant structural systems as those systems which not only have adeqate intact strength to withstand initial failure but also adequate residual strength to minimize the possibility of, and hence the consequences of, further failure. The incorporation of damage tolerance cannot be done in total isolation of the function being required of the system and the costs associated with obtaining improved damage tolerance. The approach, therefore, is to formulate multiple-objective, multi-level decision support problems (DSP), the solutions of which represent a compromise between higher costs and higher damage tolerance. Mulitple-objective decision support problems are easily solved in the linear domain. These formulations, however, include both linear and nonlinear constraints and goals, which in the past, have not been considered due to the resulting complexity. Here, researchers: (1) present a complete discussion and description of decision support problems; (2) identify what further research needs to be done in order to obtain information that is required but not known for solving problems using these models; and (3) identify what needs to be done to implement this prototype method in practice.

Beschreibung: Ocean-going vehicles and platforms are among the largest structures in the world and are subjected to relatively harsh conditions of motions and loads. Some of them, such as semi-submersible platforms, are a relatively new type of structure and hence there is no formal, well evolved and established structural design code as there is for more traditional structures. More recently, efforts have also been made to develop a design method of this type for ships and other ocean structures. One of the many advantages of a rationally based design method is versatility; it can be used for structures that have widely differing purposes, measures of merit, shapes and sizes. The purpose is to describe a rationally based design method that has been developed within the field of ocean structures, in order that persons dealing with other types of structure can judge whether and to what extent its various features may be useful for those other types. Also, even though some features may not be applicable they might stimulate some useful ideas.

Beschreibung: The random vibration of the components of the space shuttle causing internal cargo bay acoustic impingement on the payload was investigated. The import factors to be considered in the design of acoustically loaded structures are the prediction of acoustic environment, prediction of structural response to this environment, and to determine the effect of the response on the structural strength requirements. Two basic responses were analyzed. The primary structure response due to random vibration is first analyzed. The output of primary structure response is used as an input to the secondary structure to calculate the component response.

Beschreibung: The elastic membrane equations which describe the deflection of a biaxially tensioned reflective mesh from an idealized surface were developed and solved. The conditions of equilibrium of the forces acting on a membrane element furnish equations which may be used to solve a variety of problems. Configurations considered include continuous, as well as incremental mesh attachment to structural members to form shapes which are approximately parabolic or spherical.

Beschreibung: The use of microcomputers in the design of a cable catenary large space antenna system is discussed. The development of a system design capability, data base utilization, systems integration, program structure and logic, and integrated graphics output are discussed.

Beschreibung: An exceptionally elegant method for structural optimization with constraints on the static response presented by Shield and Prager is discussed. Their derivation of the optimality condition was facilitated by a reformulation of the structural elasticity equations in terms of what was then a new variational principle, the principle of stationary mutual potential energy. Their optimality condition relates the design variable to an appropriately defined mutual strain energy. An alternative but related approach, based upon the principle of stationary mutual complementary energy, presented by N. C. Haung, is also discussed. The simplicity of these principles lies in the facts that the energy functionals are stationary at the solution to the field equations and that their stationary value is proportional to the quantity to be optimized.

Beschreibung: The effects of space environments on damping materials and damping designs on flexible structures were investigated. The following items were examined: damping of flexible spacecraft appendages; composite loss factor (n sub s) vs. time in high vacuum for damped test beams and damping of flexible structures. The STEP experiments show inherent damping of flexible structures in space effective possible damping design configurations for space structures, effects of passively damped components on the system loss factor of flexible structures and the effect of space environment on properties of damping materials.

Beschreibung: Interplanetary dust particles (micrometeoroids) are expected to form well-defined craters upon impacting exposed material in space. Studying the frequency and features of these craters will provide data on the mass-flux distribution of micrometeoroids and, to a lesser extent, on the velocity magnitude and direction. This experiment will study impact craters produced by micrometeoroids on selected materials (metals and glasses in the form of thick targets) to obtain valuable technological and scientific data. Specifically, the studies will focus on determining micrometeoroid composition and mass-flux distribution. Analyses will also be made on the distribution of impact velocity vectors.

Beschreibung: A geometrically nonlinear finite element analysis of cohesive failure in typical joints is presented. Cracked-lap-shear joints were chosen for analysis. Results obtained from linear and nonlinear analysis show that nonlinear effects, due to large rotations, significantly affect the calculated mode 1, crack opening, and mode 2, inplane shear, strain-energy-release rates. The ratio of the mode 1 to mode 2 strain-energy-release rates (G1/G2) was found to be strongly affected by the adhesive modulus and the adherend thickness. The ratios between 0.2 and 0.8 can be obtained by varying adherend thickness and using either a single or double cracked-lap-shear specimen configuration. Debond growth rate data, together with the analysis, indicate that mode 1 strain-energy-release rate governs debond growth. Results from the present analysis agree well with experimentally measured joint opening displacements. Previously announced in STAR as N83-13497

Beschreibung: Studies have been conducted to develop efficient techniques to simulate crack extension and to examine various local and global fracture criteria. Of the considered criteria, the crack-tip-opening angle (CTOA) or displacement (CTOD) at a specified distance from the crack tip was shown to be most suited for modeling stable crack growth and instability during the fracture process. The results obtained in a number of studies show the necessity for studying different crack configurations when assessing the validity of any fracture criteria. One of the objectives of the present investigation is related to a critical evaluation of the CTOD growth criterion using an elastic-plastic finite element analysis under monotonic loading to failure. The analysis was found to predict three stages of crack growth behavior under monotonic loading to failure. Calculated CTOD values agreed well with experimental values for crack growth initiation.

Beschreibung: Attenuation of the load transmitted to a vehicle occupant by the structure, either by modifying structural assembly, changing geometry of its elements, or adding specific load limiting devices to help dissipate kinetic energy was studied. General aviation aircraft have fuselage subfloors of a built up structure which are generally very stiff perpendicular to the floor of the cabin. The subfloor structure, designed to crush at an appropriate force level, can be used to advantage in a crash by dissipating energy through plastic buckling of the floor beams and frames. Simple closed form solutions to predict the mean crushing force levels of subfloor designs is useful in engineering practice. The crushing process of thin walled, plate formed, open structures with particular emphasis on L and cruciform shapes was analyzed. Lower and upper bound solutions for the mean crushing strength of cruciforms are obtained by considering modes of deformation which account for both bending and extensional deformation. It is the importance of extensional deformation to the energy absorption process, representing at least one third of the dissipated energy is shown. Previously announced in STAR as N82-33765

Beschreibung: The methods for predicting the strength of composite laminates with fastener holes are reviewed for the cases of unloaded as well as loaded holes. Three categories of methods are discussed: (1) the hole-boundary stress (HBS) methods which compare the peak stresses and the laminate strength; (2) the linear elastic fracture (LEFM) methods which assume cracks emanating from the hole and predict failure when the stress intensity factor for a crack equals the laminate fracture toughness; and (3) two different two-parameter (TP) methods: the average-stress (ASTP) method, which predicts failure when the average stress over a distance from the hole equals the laminate strength; and the point-stress (PSTP) Whitney-Nuismer (1974) approach, which predicts failure when the stress near the hole equals the material strength. The PSTP is relatively accurate and is by far the most widely used of all the prediction methods. However, for large ranges of variables and cases, the current strength predictions may not always be accurate.

Beschreibung: Optimality criteria methods take advantage of some concepts as those of statically determinate or indeterminate structures, and certain variational principles of structural dynamics, to develop efficient algorithms for the sizing of structures that are subjected to stiffness-related constraints. Some of the methods and iterative strategies developed over the last decade for calculations of the Lagrange multipliers in stressand displacement-limited problems, as well as for satisfying the appropriate optimality criterion, are discussed. The application of these methods are illustrated by solving problems with stress and displacement constraints.

Beschreibung: The stiffened composite structural panel analysis and sizing code designated 'PASCO' encompasses both the generality required for the exploitation of composite materials' design flexibility and an accurate buckling analysis for the detection of complex buckling modes. PASCO can accordingly design for buckling, frequency, material strength, and panel stiffness requirements. Attention is given to an additional thermal loading design capability. Design studies illustrate the importance of the multiple load condition capability when thermal loads are present.

Beschreibung: A detailed comparison is presented of the predicted eigenfrequencies of twisted rotating plates as obtained by using two different shape functions. Primarily, rotating twisted plates of two different aspect ratios and two different thickness ratios are considered. The effects of rotation are included by using a 'stress smoothing' technique when calculating the augmented stiffness matrix. In addition, the effects of Coriolis acceleration, contributions from membrane behavior, setting angle and sweep angle are considered. The effects of geometric nonlinearity are briefly discussed. Finally, results of a brief study of cambered plates are presented.

Beschreibung: Delamination growth in compressively loaded composite laminates was studied analytically and experimentally. The configuration used was a laminate with an across-the-width delamination. An approximate super-position stress analysis was developed to quantify the effects of various geometric, material, and load parameters on mode 1 and mode 2 strain energy release rates G sub 1 and G sub 2, respectively. Calculated values of G sub 1 and G sub 2 were then compared with measured cyclic delamination growth rates to determine the relative importance of G sub 1 and G sub 2. High growth rates were observed only when G sub 1 was large. However, slow growth was observed even when G sub 1 was negligibly small. This growth was apparently due to a large value of G sub 2.

Beschreibung: A special three-dimensional element based on the total Lagrangian description of the motion of a layered anisotropic composite medium is developed, validated and employed to analyze laminated anisotropic composite shells. The element contains the following features: geometric nonlinearity, dynamic (transient) behavior and arbitrary lamination scheme and lamina properties. Numerical results of nonlinear bending, natural vibration, and transient response are presented to illustrate the capabilities of the element.

Beschreibung: A technique is presented for computing a set of normal modes from a set of measured complex modes. The number of elements in the modal vectors, which is equal to the number of measurements, can be larger than the number of modes under consideration. It is also shown that the practice of normal mode approximation to complex modes can lead to very large errors when the modes are too complex. A numerical example and a simulated experiment illustrate the concepts discussed and support the theory presented.

Beschreibung: The finite element method, modal component synthesis, and the use of fast Fourier transformation were key developments in structural dynamics in the past 15 to 20 years. Current areas requiring additional effort include: (1) the correct calculation of modal shape and natural frequencies for complex structures; (2) the correlation of math models with test data; (3) the establishment of a criteria for "goodness" of the correlation between analysis and test; (4) the selection of the correct displacement functions when using computer programs for modal synthesis; (5) accuracy of response calculations; and (6) the inverse problem of determining the force problem from the response data. Trends identified include the use of distributed computing, greater reliance on analysis, and the possible use of artificial intelligence techniques, or some way of feeding back information, to provide solution guidance to engineers.

Beschreibung: The use of automatic multi-stage substructing analysis is demonstrated for a hypothetical case of a GAS container supported by structural channels with a simulated experimental package inside the container. The GAS program purpose is stated and potential candidate structures to support experimental packages are discussed. The GAS container model and the substructuring analysis capabilities of NASTRAN make it possible to study the experiments inside the container as well as the design constraints resulting from the support structures holding the containers. The use of substructuring in the GAS program could be an important factor in increasing the number of flight opportunities.

Beschreibung: An eight node curved thin shell slement was tested. The element is based on the degenerate solid concept and the mixed formulation with the independent inplane and transverse shear strains. The number of unknown parameters in the assumed strains is chosen to alleviate the spurious constaining or locking effect. It is indicated that for a pinched cylindrical shell with diaphragmed ends and fixed ends the present element shows good performance.

Beschreibung: During dynamic torsion of beam elements, consideration of nonuniform warping effects involves a more general technical formulation then that of Saint-Venant. Nonclassical torsion constants appear in addition to the well known torsional rigidity. The adaptation of the boundary integral element method to the calculation of these constants for general section shapes is described. The suitability of the formulation is investigated with some examples of thick as well as thin walled cross sections.

Beschreibung: An effort to apply the reduced basis method to nonlinear transient thermal analysis is described. The method combines the classical Rayleigh-Ritz and modal superposition techniques with contemporary finite element methods to retain modeling versatility as the degrees of freedom in a problem are reduced. The essence of the method is to use a few thermal modes from eigenvalue analyses as basis vectors to represent the temperature response for a given thermal problem similar to the use of vibration modes to represent displacements in a dynamic response problem. Approximate temperature distributions were obtained using the reduced basis method for a small section of the Shuttle Orbiter lower wing undergoing reentry heating. Good agreement was obtained between the reduced basis method solutions and full system solutions with reductions in the degrees of freedom of up to a factor of four. The good agreement indicates the reduced basis method has the potential for significant reduction in computing effort for thermal analysis; however, considerable work remains to determine techniques for selecting the type and number of basis vectors needed for approximate solutions to more complex transient thermal problems.

Beschreibung: Aluminum alloys of types 1100, 3003, 5052, 6061, and 2024 were used to study the sensitivity of the acousto-elastic constant to changes in the microstructure. Results show that there is a strong relationship between the acousto-elastic constants and the yield strength and hardness. This relationship depends on whether the alloy is strain hardened or precipitation hardened. In strain hardened alloys, the constants increase as the amount of solid solution is decreased, while the behavior is the opposite in precipitation hardened alloys.

Beschreibung: The effect of nonlinearity on the higher harmonic control (HHC) of helicopter vibration is investigated using a nonlinear aeroelastic simulation. A nonlinear solution is proposed which relates the HHC inputs to vibration outputs on the basis of a Volterra functional series. The Volterra series solution is shown to reduce to a vector polynomial equation relating HHC inputs to vibration outputs at any harmonic frequency. The nonlinear transfer relationship is identified from a nonlinear vibration analysis computer program, and the identification model is examined in detail. Improvements to current HHC algorithms are presented, and several Kalman filter divergence problems are quantified.

Beschreibung: A general crack opening stress equation is presented which may be used to correlate crack growth rate data for various materials and thicknesses, under constant amplitude loading, once the proper constraint factor has been determined. The constraint factor, alpha, is a constraint on tensile yielding; the material yields when the stress is equal to the product of alpha and sigma. Delta-K (LEFM) is plotted against rate for 2024-T3 aluminum alloy specimens 2.3 mm thick at various stress ratios. Delta-K sub eff was plotted against rate for the same data with alpha = 1.8; the rates correlate well within a factor of two.

Beschreibung: The transient response of a 0.4 by 0.6 cm rectangular bore rail accelerator was analyzed by a three dimensional finite element code. The copper rail deflected to a peak value of 0.08 mm in compression and then oscillated at an amplitude of 0.02 mm. Simultaneously the insulating side wall of glass fabric base, epoxy resin laminate (G-10) was compressed to a peak value of 0.13 mm and rebounded to a steady state in extension. Projectile pinch or blowby due to the rail extension or compression, respectively, can be identified by examining the time history of the rail displacement. The effect of blowby was most significant at the side wall characterized by mm size displacement in compression. Dynamic stress calculations indicate that the G-10 supporting material behind the rail is subjected to over 21 MPa at which the G-10 could fail if the laminate was not carefully oriented. Results for a polycarbonate resin (Lexan) side wall show much larger displacements and stresses than for G-10. The tradeoff between the transparency of Lexan and the mechanical strength of G-10 for sidewall material is obvious. Displacement calculations from the modal method are smaller than the results from the direct integration method by almost an order of magnitude, because the high frequency effect is neglected. Previously announced in STAR as N83-35412

Beschreibung: (Previously announced in STAR as N81-27202)

Beschreibung: (Previously cited in issue 12, p. 2022, Accession no. A81-29471)

Beschreibung: The Guyan reduction refers to a method used to reduce the number of degrees of freedom in a structural model for dynamic analysis. Experience shows that, if the method is properly employed, then this reduction method does in fact provide a "reasonably" accurate approximation of the dynamic characteristics of the unreduced model. A method that provides an accurate estimate of the error in each mode of the reduced eigenvalue problem and, in addition, gives first order correction terms that greatly improve the accuracy of the eigenvectors and eigenvalues is presented. The method is demonstrated by standard COSMIC NASTRAN DAMP alters to rigid format 3, real normal mode analysis. Comparative computer time of modal extraction versus error analysis is discussed for the VAX-11/780 version of COSMIC NASTRAN.

Beschreibung: The concept of expressing test modes as a linear combination of analytical modes was applied to the prediction of corrective terms in math model mass and stiffness. Test data for the Space Shuttle quarter scale solid rocket booster were analyzed by this method and significant improvements in frequency and mode shap correlation are noted. The applicability of the method is demonstrated.

Beschreibung: The solution of axisymmetric acoustic fluid structure interaction problems, employing the NASTRAN computer program is presented. A previously developed 3-D Cartesian Coordinates pressure element formulation is adapted especially for axisymmetric elements. Analogous to the 3-D Cartesian Coordinate predecessor, the fluid portion of the problem is modeled with finite elements wherein one of the displacement components serves as a dummy variable for the pressure unknowns. Two alternatives for implementation of the analogy are presented: (1) an approximate method by which dummy values of G, and nu are used to approximately invoke the analogy wherein the accuracy of the approximation is made as close as desired to the proper analogy within an arbitrary small parameter epsiton; (2) an exact method whereby the NASTRAN FORTRAN coding is slightly changed to invoke the analogy exactly. Comparison of the finite element solution to the exact solution to the same problem is given.

Beschreibung: Two specific NASTRAN preprocessors and postprocessors are examined. A postprocessor for dynamic analysis and a graphical interactive package for model generation and review of resuls are presented. A computer program that provides response spectrum analysis capability based on data from NASTRAN finite element model is described and the GIFTS system, a graphic processor to augment NASTRAN is introduced.

Beschreibung: Several improvements and enhancements recently made to NASTRAN are described. Some of the more important features are: streamlined rigid formats; improved rigid formats; changes related to plotting; checking of required PARAM bulk data cards; checkpoint/restart capability; unsorted and sorted bulk data deck echo; automatic output of the DMAP source listing; elimination of link switching caused by use of utility modules; paging the NASTRAN output; processing of mixed record data blocks by INPUT2/OUTPUT2 modules; module execute flag included in the OSCAR listing; and use of the multiple XDMAP cards in the DMAP. It is concluded that these changes increase the usefulness of the program.

Beschreibung: The theory of acoustic propagation in strained media is examined, with particular emphasis on rod (bolt) geometries. The continuous wave (CW) approach is the basis of the study, and the theory is developed from a frequency domain analysis standpoint in order to obtain an applied stress/normalized frequency shift relationship. CW measurements may be influenced by such factors as propagation effects, mode conversion, frequency, material properties, and geometry. After the first loading cycle, axial stress measurements for a preloading with an initial frequency of 4.995 36 MHz dropped to 4.989 19 MHz, indicating a 6.17 kHz change. CW and pseudo-CW ultrasonic techniques are found to be reliable for axial stress measurements, and acoustic attenuation measurements correlated to residual stress fields may possibly involve transducer phase cancellation. It is thus concluded that signal drop is an artifact of the transducer directivity, rather than an actual acoustic power decrease.

Beschreibung: The suggestion is made that the standard compact specimen (with opening displacement measured at the crack mouth) may be entirely suitable for J-integral determinations if a very simple conversion factor is used. Experimental determination of J-integral values requires the measurement of displacements at the points of load application. For the compact specimen this is a difficult task. On the basis of studies reported by Newman (1979) and Fisher and Buzzard (1980), it is suggested that for any J-based test the standard compact specimen can be used. A very good approximation to the load point displacement (within 3.4 percent) can be obtained by measuring the crack mouth displacement and multiplying by 0.773.

Beschreibung: The checkpoint/restart capability available in NASTRAN is very sophisticated. Improvements and enhancements to this capability made with a view to increasing its efficiency and usefulness are considered. Some important features resulting from these changes are discussed. In particular, the different types of restarts available in NASTRAN are described and how they are handled both in the rigid format and DMAP environments explained. The output to restart runs are also illustrated.

Beschreibung: Preliminary plans for the conversion of NASTRAN to DENELCOR's heterogeneous element processor (HEP) are presented. First, a brief history of computer architecture and the architecture of the HEP computer system are discussed. Second, a description of the HEP computer system is provided. Lastly, the preliminary NASTRAN conversion plans for link management, I/O management, memory management, and code optimization are discussed.

Beschreibung: A new direct matrix abstract program for NASTRAN written to calculate internal stresses and airloads for a flexible wing is described. The difficulties encountered in interfacing the doublet lattice solution to the aerodynamic problem to the finite element solution to the structural problem are discussed. A brief numerical example is included.

Beschreibung: The NASTRAN structural analysis computer program may be used, without modification, to solve two dimensional Poisson equations such as arise in the classical Saint Venant torsion problem. The nonhomogeneous term (the right-hand side) in the Poisson equation can be handled conveniently by specifying a gravitational load in a "structural" analysis. The use of an analogy between the equations of elasticity and those of classical mathematical physics is summarized in detail.

Beschreibung: The use of linear rigid formats in COSMIC NASTRAN without DMAP procedures for the analysis of nonlinear propeller structures is described. Approaches for updating geometry and applying follower forces for incremental loading are demonstrated. The COSMIC NASTRAN rigid formats and other independent finite element programs are compared. The comparisons include results from the four approaches for updating the geometry using RIGID FORMAT 1, RIGID FORMATS 4 and 13, MARC and MSC/NASTRAN. It is shown that user friendly updating approaches can be used to predict the large displacements and instability of these nonlinear structures. The approaches are easily implemented by the user and predict conservative results.

Beschreibung: An interactive review system that addresses the problems of model display, model error checking, and postprocessing is described. The menu driven system consists of four programs whose advantages and limitations are detailed. The interface between NASTRAN and MOVIE-BYU, the modifications required to make MOVIE usable in a finite element context, and the resulting capabilities of MOVIE as a graphics postprocessor for NASTRAN are illustrated.

Beschreibung: The interlaminar normal stress distributions along the interface between the +45 deg and -45 deg plies of a graphite/epoxy laminate, obtained by various investigators, were found to disagree in both magnitude and sign. The reliability of the displacement-formulated finite element method in analyzing the edge-stress problem of a composite laminate is investigated. The history of the edge-stress problem is reviewed, and two well-known elasticity problems, one involving a stress discontinuity and one a singularity, are analyzed. The finite element analysis in these problems yields accurate stress distributions everywhere except in two elements closest to the stress discontinuity or singularity. Stress distributions for a + or -45 deg ply laminate near the singularity were similar to those of the two elasticity problems, demonstrating the methods, accuracy for calculating interlaminar stresses in composite laminates. The disagreement between the numerical methods was attributed to the unsymmetric stress tensor at singularity.

Beschreibung: The unified constitutive theories for application to typical isotropic cast nickel base supperalloys used for air-cooled turbine blades were evaluated. The specific modeling aspects evaluated were: uniaxial, monotonic, cyclic, creep, relaxation, multiaxial, notch, and thermomechanical behavior. Further development of the constitutive theories to model thermal history effects, refinement of the material test procedures, evaluation of coating effects, and verification of the models in an alternate material will be accomplished in a follow-on for this base program.

Beschreibung: A state-of-the-art review of applicable constitutive models with selection of two for detailed comparison with a wide range of experimental tests was conducted. The experimental matrix contained uniaxial and biaxial tensile, creep, stress relaxation, and cyclic fatigue tests at temperatures to 1093 C and strain rates from .0000001 to .001/sec. Some nonisothermal cycles will also be run. The constitutive models will be incorporated into the MARC finite element structural analysis program with a demonstration computation made for advanced turbine blade configuration. In the code development work, particular emphasis is being placed on developing efficient integration algorithms for the highly nonlinear and stiff constitutive equations. Another area of emphasis is the appropriate and efficient methodology for determing constitutive constants from a minimum extent of experimental data.

Beschreibung: Static aerothermoelastic design/analysis of axial-flow compressors, modal flutter analysis of axial-flow turbomachines, forced vibration analysis of rotating cyclic structures and modal flutter analysis of advanced turbopropellers with highly swept blades are four new capabilities developed and implemented in NASTRAN Level 17.7. The contents, applicability and usefulness of these capabilities which were developed and documented under the sponsorship of NASA's Lewis Research Center are discussed. Overall flowcharts and selected examples are presented.

Beschreibung: COSMIC/NASTRAN was converted to the CRAY computer systems. The CRAY version is currently available and provides users with access to all of the machine independent source code of COSMIC/NASTRAN. Future releases of COSMIC/NASTRAN will be made available on the CRAY soon after they are released by COSMIC.

Beschreibung: Computer aided engineering systems are invaluable tools in performing NASTRAN finite element analysis. These techniques are implemented in both the pre-processing and post-processing phases of the NASTRAN analysis. The finite element model development, or pre-processing phase, was automated with a computer aided modeling program called Supertabl, and the review and interpretation of the results of the NASTRAN analysis, or post-processing phase, was automated with a computer aided plotting program called Output Display. An intermediate program, Nasplot, which was developed in-house, has also helped to cut down on the model checkout time and reduce errors in the model. An interface has been established between the finite element computer aided engineering system and the Learjet computer aided design system whereby data can be transferred back and forth between the two. These systems have significantly improved productivity and the ability to perform NASTRAN analysis in response to product development requests.

Beschreibung: A methodology that supports forced transient response dynamic solutions when both static and kinetic friction effects are included in a structural system model is described. Modifications that support this type of nonlinear transient response solution are summarized for the transient response dynamics (TRD) NASTRAN module. An overview of specific modifications for the NASTRAN processing subroutines, INITL, TRD1C, and TRD1D, are described with further details regarding inspection of nonlinear input definitions to define the type of nonlinear solution required, along with additional initialization requirements and specific calculation subroutines to successfully solve the transient response problem. The extension of the basic NASTRAN nonlinear methodology is presented through several stages of development to the point where constraint equations and residual flexibility effects are introduced into the finite difference Newmark-Beta recurrsion formulas. Particular emphasis is placed on cost effective solutions for large finite element models such as the Space Shuttle with friction degrees of freedom between the orbiter and payloads mounted in the cargo bay. An alteration to the dynamic finite difference equations of motion is discussed, which allows one to include friction effects at reasonable cost for large structural systems such as the Space Shuttle. Data are presented to indicate the possible impact of transient friction loads to the payload designer for the Space Shuttle. Transient response solution data are also included, which compare solutions without friction forces and those with friction forces for payloads mounted in the Space Shuttle cargo bay. These data indicate that payload components can be sensitive to friction induced loads.

Beschreibung: The results of a study to determine the accuracy of the three dimensional solid elements available in NASTRAN for predicting displacements is presented. Of particular interest in the study is determining how to effectively use solid elements in analyzing thick optical mirrors, as might exist in a large telescope. Surface deformations due to thermal and gravity loading can be significant contributors to the determination of the overall optical quality of a telescope. The study investigates most of the solid elements currently available in either COSMIC or MSC NASTRAN. Error bounds as a function of mesh refinement and element aspect ratios are addressed. It is shown that the MSC solid elements are, in general, more accurate than their COSMIC NASTRAN counterparts due to the specialized numerical integration used. In addition, the MSC elements appear to be more economical to use on the DEC VAX 11/780 computer.

Beschreibung: Some innovative techniques applicable to sensitivity analysis of discretized structural systems are reviewed. These techniques include a finite-difference step-size selection algorithm, a method for derivatives of iterative solutions, a Green's function technique for derivatives of transient response, a simultaneous calculation of temperatures and their derivatives, derivatives with respect to shape, and derivatives of optimum designs with respect to problem parameters. Computerized implementations of sensitivity analysis and applications of sensitivity derivatives are also discussed. Finally, some of the critical needs in the structural sensitivity area are indicated along with Langley plans for dealing with some of these needs.

Beschreibung: In developing the constitutive equations an interdisciplinary approach is being pursued. Specifically, both metallurgical and continuum mechanics considerations are recognized in the formulation. Experiments will be utilized to both explore general qualitative features of the material behavior that needs to be modeled and to provide a means of assessing the validity of the equations being developed. The model under development explicitly recognizes crystallographic slip on the individual slip systems. This makes possible direct representation of specific slip system phenomena. The present constitutive formulation takes the anisotropic creep theory and incorporates two state variables into the model to account for the effect of prior inelastic deformation history on the current rate-dependent response of the material.

Beschreibung: A brief overview of the status of the fatigue and fracture programs is given. The programs involve the development of appropriate analytic material behavior models for cyclic stress-strain-temperature-time/cyclic crack initiation, and cyclic crack propagation. The underlying thrust of these programs is the development and verification of workable engineering methods for the calculation, in advance of service, of the local cyclic stress-strain response at the critical life governing location in hot section compounds, and the resultant crack initiation and crack growth lifetimes.

Beschreibung: For economic reasons, the steam drive for a large compressor was replaced by a large synchronous electric motor. Due to the resulting large increase in mass and because the unit was mounted on a steel frame approximately 18 feet above ground level, it was deemed necessary to determine if a steady state or transient vibration problem existed. There was a definite possibility that a resonant or near resonant condition could be encountered. The ensuing analysis, which led to some structural changes as the analysis proceeded, did not reveal any major steady state vibration problems. However, the analysis did indicate that the system would go through several natural frequencies of the support structure during start-up and shutdown. This led to the development of special start-up and shutdown procedures to minimize the possibility of exciting any of the major structural modes. A coast-down could result in significant support structure and/or equipment damage, especially under certain circumstances. In any event, dynamic field tests verified the major analytical results. The unit has now been operating for over three years without any major vibration problems.

Beschreibung: Seismic analysis is a technique which pertains to loading described in terms of boundary accelerations. Earthquake shocks to buildings is the type of excitation which usually comes to mind when one hears the word seismic, but this technique also applied to a broad class of acceleration excitations which are applied at the base of a structure such as vibration shaker testing or shocks to machinery foundations. Four different solution paths are available in NASTRAN for seismic analysis. They are: Direct Seismic Frequency Response, Direct Seismic Transient Response, Modal Seismic Frequency Response, and Modal Seismic Transient Response. This capability, at present, is invoked not as separate rigid formats, but as pre-packaged ALTER packets to existing RIGID Formats 8, 9, 11, and 12. These ALTER packets are included with the delivery of the NASTRAN program and are stored on the computer as a library of callable utilities. The user calls one of these utilities and merges it into the Executive Control Section of the data deck to perform any of the four options are invoked by setting parameter values in the bulk data.

Beschreibung: A user's guide to the COSMIC/NASTRAN free field input for the Bulk Data section of the NASTRAN program is proposed. The free field input is designed to be user friendly and the user is not forced out of the computer system due to input errors. It is easy to use, with only a few simple rules to follow. A stand alone version of the COSMIC/NASTRAN free field input is also available. The use of free field input is illustrated by a number of examples.

Beschreibung: The annual static loading tests were made on the assembled wing/fuselage structure of the RP-1 sailplane. Simple wing bending and wing bending/torsion tests up to about four G's were made, using sand bag loading on the inverted aircraft. Bending a torsion deflections were measured and compared to those obtained in previous years' tests. It appears that the structure is retaining its original strength and stiffness very well. This aircraft has been disassembled and stored on the Jonsson Engineering Center under ambient, indoor conditions of temperature and humidity.

Beschreibung: Progress has been made on the design fabrication and installation of a tension carry-through linkage between the aft parts of the port and starboard wings to resist forward bending deflection on the RP-2 sailplane. In addition, towhook/release mechanisms, landing gear and wheel brake assembly, compound curved sandwich composite fuselage shells and an enclosed trailer to house and transport the complete disassembled aircraft, have all undergone various stages of design, fabrication, installation and testing.

Beschreibung: The initiation and growth of small cracks (5-500 microns m) from edge notches in 2024-T3 aluminum alloy sheets were studied under constant amplitude loading. Two methods were used to measure crack shape and size. In the first method, striation marker bands were periodically formed along the crack front by interrupting the constant amplitude loading by either an elevated R-ratio load sequence, or by an overload sequence. In the second method, the surface crack length was monitored by taking surface replicas at regular intervals. The marker band techniques did not provide reliable crack length and crack shape information for cracks smaller than 2 mm. The replica technique provided accurate information for surface crack length at all crack lengths, and fracture tests on specimens with small cracks provided crack-shape information. Crack growth rates were plotted against the stress intensity factor ranges. The results exhibited the small crack effect, in that the small cracks grew faster than large cracks at the same stress-intensity factor range. A crack closure model was also used to analyze the growth of small cracks from small (inclusion) defects at the notch surface.

Beschreibung: A nonliner series summation technique was combined with Chien's small parameter perturbation technique to solve the problem of the finite deflection of a simply supported circular plate subjected to a uniform transverse load. Problems involving finite deflections of plates with simply supported or free edges were regarded as almost intractable. The great advantage of incorporating the summation method into the solution procedure is demonstrated.

Beschreibung: The susceptibility to induced torsional response of symmetric building structures with nonliner resisting elements was investigated. Stability curves show the effect of the arrangement of the load resisting elements on induced torsional coupling in these nonliner but other wise symmetric structures. Universal upper and lower bound instability curves are also derived; these identify the susceptibility to torsional coupling of symmetric structures with different stiffness arrangements but which have equal mass and total lateral stiffness, and which are intended to model alternative structural strategies for lateral load resistance.

Beschreibung: A method for the minimum weight design of practical planar frameworks under both service and ultimate loading conditions is presented. Acceptable elastic stresses and displacements are ensured at the service load level while, simultaneously, adequate safety against plastic collapse is ensured at the ultimate load level. The features of the design method for an industrial steel mill building are illustrated.

Beschreibung: An exact zooming technique which employs static condensation and exact structural reanalysis methods was developed. Successive application of static condensation reduces the system to one that is only associated with the degrees of freedom (dof) of the original model. Application of an exact static reanalysis technique permits the displacements at the dof of the original model that are contained in the zoomed portion of the structure to be obtained first. The response external to the zoom, as well as the response of additional dof within various levels of zooming, is computed. With the triangular factor of the stiffness matrix of the original system available, this approach involves only the solution of a system of equations of small order.

Beschreibung: A finite element analysis emulator providing a basis for efficiently establishing an optimum computer implementation strategy when many calculations are involved is described. The SCOPE emulator determines computer resources required as a function of the structural model, structural load-deflection equation characteristics, the storage allocation plan, and computer hardware capabilities. Thereby, it provides data for trading analysis implementation options to arrive at a best strategy. The models contained in SCOPE lead to micro-operation computer counts of each finite element operation as well as overall computer resource cost estimates. Application of SCOPE to the Memphis-Arkansas bridge analysis provides measures of the accuracy of resource assessments. Data indicate that predictions are within 17.3 percent for calculation times and within 3.2 percent for peripheral storage resources for the ELAS code.

Beschreibung: At high strain rates the heat produced by plastic deformation can give rise to a rate dependent response even if the material has rate independent constitutive equations. This effect has to be evaluated when interpreting a material test, or else it could erroneously be ascribed to viscosity. A general thermodynamic theory of tensile testing of elastic-plastic materials is given in this paper; it is valid for large strain at finite strain rates. It enables discovery of the parameters governing the thermodynamic strain rate effect, provides a method for proper interpretation of the results of the tests of dynamic plasticity, and suggests a way of planning experiments in order to detect the real contribution of viscosity.

Beschreibung: A number of viscoplastic constitutive theories and a conventional constitutive theory are evaluated and compared in their ability to predict nonlinear stress-strain behavior in gas turbine engine components at elevated temperatures. Specific application of these theories is directed towards the structural analysis of combustor liners undergoing transient, cyclic, thermomechanical load histories. The combustor liner material considered in this study is Hastelloy X. The material constants for each of the theories (as a function of temperature) are obtained from existing, published experimental data. The viscoplastic theories and a conventional theory are incorporated into a general purpose, nonlinear, finite element computer program. Several numerical examples of combustor liner structural analysis using these theories are given to demonstrate their capabilities. Based on the numerical stress-strain results, the theories are evaluated and compared.

Beschreibung: A semiimplicit dynamic relaxation technique for solution of the nonlinear structural equlibrium equation is presented. A previously presented basic transient response analysis algorithm is employed, permitting use of one solution method and one software module for both static and dynamic analyses. A theoretical comparison of the method with explicit dynamic relaxation techniques shows that it offers a substantially improved convergence property without additional computational overhead.

Beschreibung: The Finite Element Machine at the NASA Langley Research Center is a prototype computer designed to support parallel solutions to structural analysis problems. The hardware architecture and support software for the machine, initial solution algorithms and test applications, and preliminary results are described. Directions for future work are presented.

Beschreibung: Alternatives to Gaussian integration methods for multidimensional regions are presented. These rules preserve the convergence behavior of the exact integrated element but require fewer evaluation points than the Gauss methods. Numerical examples are given to verify the behavior of the new integration rules.

Beschreibung: A boundary element method computer program developed for heat transfer analysis of two dimensional composite structures is described. The program runs on a time share mode and interacts with the user for multirun analysis. During a run, the geometry can be modified interactively by the user as many times as desired by using various options available and the new results printed or plotted. A concept of plotting the results for boundary element method is introduced. The advantage of such a program over the finite element method for simple design problems is demonstrated.

Beschreibung: The spatial formulation of the elastoplastic dynamic problem for finite deformations is considered. A thermodynamic argument leads to an additive decomposition of the spatial rate of deformation tensor and allows an operator split of the evolutionary equations of the problem into elastic and plastic parts. This operator split is taken as the basis for the definition of a global product algorithm. In the context of finite element discretization the product algorithm entails, for every time step, the solution of a nonlinear elastodynamic problem followed by the application of plastic algorithms that operate on the stresses and internal variables at the integration points and bring in the plastic constitutive equations. Suitable plastic algorithms are discussed for the cases of perfect and hardening plasticity and viscoplasticity. The proposed formalism does not depend on any notion of smoothness of the yield surface and is applicable to arbitrary convex elastic regions, with or without corners. The stabiity properties of the global product algorithm are shown to be identical to those of the algorithm used for the integration of the nonlinear elastodynamic problem. Numerical examples illustrate the accuracy of the method.

Beschreibung: The dynamic stress concentration manifested around a lined cylindrical tunnel buried in an infinitely extending linear elastic or viscoelastic medium due to the passage of transient disturbances was investigated. Plane strain is assumed to hold and the transient disturbances can be of any arbitrary time variation. The boundary element method formulated in the Laplace transform domain is employed. Isoparametric boundary elements are used in the discretization of the liner and tunnel surfaces. Viscoelastic material behavior can be readily obtained from the linear elastic case in the Laplace transform domain through the use of the correspondence principle. The transient solution is recovered by numerical inversion of the solution obtained in the transformed domain.

Beschreibung: Adhesives are commonly characterized only by their static strength even though they are used in structural joints that are subjected to fatigue loads. This paper reviews the relationship between static and fatigue strength for four different specimen types: single-lap-shear, edge-delamination, double cantilever beam, and cracked-lap-shear. It was found that the ratio of static strength to fatigue strength varied from 2.3 to 4.7, depending on the adhesive and specimen configuration.

Beschreibung: A method for computation of reflective dihedral symmetry in symmetrical structures under nonsymmetric loads is described. The method makes it possible to confine the analysis to a half, a quarter, or an octagonal segment. The symmetry of elastic deformation is discussed, and antisymmetrical deformation is distinguished from nonsymmetrical deformation. Modes of deformation considered are axial, bending, membrane, and torsional deformation. Examples of one and two dimensional elements are presented and extended to three dimensional elements. The method of setting up a problem within NASTRAN is discussed. The technique is applied to a thick structure having quarter symmetry which was modeled with polyhedra and subjected to five distinct loads having varying degrees of symmetry.

Beschreibung: The piece-wise linear analysis option of the NASTRAN code was used to analyze a photoplastic model for a sliding breech mechanism. A two dimensional finite element representation for the breech ring was chosen and the material was made of polycarbonate resin. The aluminum block was regarded as rigid and the width of contact was assumed to remain unchanged during loading. The displacements and stresses in the breech ring were obtained for loading in the elastic as well as plastic range. The maximum tensile stresses before and after complete unloading were obtained and compared with numerical and experimental results.

Beschreibung: The theoretical prediction of the bead area contact load at the tire wheel interface using NASTRAN is reported. The application of the linear code to a basically nonlinear problem results in excessive deformation of the structure and the tire-wheel contact conditions become impossible to achieve. A psuedo-nonlinear approach was adopted in which the moduli of the cord reinforced composite are increased so that the computed key deformations matched that of the experiment. Numerical results presented are discussed.

Beschreibung: The use of a prolate spheroidal harmonic expansion to compute far field results in magnetics problems with the DTNSRDC version of NASTRAN is demonstrated. When field problems with infinite exterior domains are solved by the finite element method, the domain must be modeled to infinity. The density of the finite element mesh usually decreases as the distance from the structure increases, thus degrading the results in the far field.

Beschreibung: The history of the development of the NASTRAN computer program, a general purpose finite element code for structural analysis, is described. The need for research programs to improve analysis of structures, and the writing of a computer program to give numerical solutions for shell behavior, were the impetus for the program design. The use of finite elements to obtain engineering solutions was introduced. The architecture, solution structure, DMAP language, decomposition technique for banded matrices with active columns, general purpose plotter, engineering data inputs, elastic element routines, programmer manuals, of NASTRAN's system design are described.

Beschreibung: An analytical investigation of the equilibrium of wrinkling films is conducted. Zak (1979) has shown that wrinkling occurs in connection with the instability of a smooth film having no resistance to bending in the case of compression. The governing equation for the equilibrium of a film with possible regions of wrinkling is considered. The introduction of fictitious stress reduces the governing equation to a form which formally coincides with the governing equation for a string. Equilibrium conditions in the case of an absence of external forces are explored, taking into account the stretching of a semispherical film, the torsion of a convex film of revolution, and stress singularities. A study is conducted of the equilibrium under conditions in which external forces normal to the surface of a film are present. Attention is also given to the equilibrium in a potential field.

Beschreibung: The results of a three-dimensional, geometrically nonlinear, finite-element analysis of the bending of cross-ply laminated anisotropic composite plates are presented. Individual laminae are assumed to be homogeneous, orthotropic and linearly elastic. A fully three-dimensional isoparametric finite element with eight nodes (i.e. linear element) and 24 degrees of freedom (three displacement components per node) is used to model the laminated plate. The finite element results of the linear analysis are found to agree very well with the exact solutions of cross-ply laminated rectangular plates under sinusoidal loading. The finite element results of the three-dimensional, geometrically nonlinear analysis are compared with those obtained by using a shear deformable, geometrically nonlinear, plate theory. It is found that the deflections predicted by the shear deformable plate theory are in fair agreement with those predicted by three-dimensional elasticity theory; however stresses were found to be not in good agreement.