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  • 1
    Electronic Resource
    Electronic Resource
    Arch shape optimization using force approximation methods (1990)
    Springer
    Structural and multidisciplinary optimization 2 (1990), S. 193-201 
    Details
    ISSN: 1615-1488
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The objective of this paper is to provide a method of optimizing areas of the members as well as the shape of both two-hinged and fixed arches. The design process includes satisfaction of combined stress constraints under the assumption that the arch ribs can be approximated by a finite number of straight members. In order to reduce the number of detailed finite element analyses, the Force Approximization Method is used. A finite element analysis of the initial structure is performed and the gradients of the member end forces (axial, bending moment) are calculated with respect to the areas and nodal coordinates. The gradients are used to form an approximate structural analysis based on first order Taylor series expansions of the member end forces. Using move limits, a numerical optimizer minimizes the volume of the arch with information from the approximate structural analysis. Numerical examples are presented to demonstrate the efficiency and reliablity of the proposed method for shape optimization. It is shown that the number of finite element analysis is minimal and the procedure provides a highly efficient method of arch shape optimization.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01748223
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Optimum design of trusses with discrete sizing and shape variables (1993)
    Springer
    Structural and multidisciplinary optimization 6 (1993), S. 79-85 
    Details
    ISSN: 1615-1488
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract The objective here is to present a method for optimizing truss structures with discrete design variables. The design variables are considered to be sizing variables as well as coordinates of joints. Both types of variables can be discrete simultaneously. Mixed continuous-discrete variables can also be considered. To increase the efficiency of the method, the structural responses, such as forces and displacements are approximated in each design cycle. The approximation of responses is carried out with respect to the design variables or their reciprocals. By substituting these approximate functions of the responses into the original design problem, an explicit high quality approximation is achieved, the solution of which does not require the detailed finite element analysis of the structure in each sub-optimization iteration. First it is assumed that all the design variables are continuous and a continuous variable optimization is performed. With the results of this step, the branch and bound method is employed on the same approximate problem to achieve a discrete solution. The numerical results indicate that the method is efficient and robust in terms of the required number of structural analyses. Several examples are presented to show the efficiency of the method.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01743339
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  • 3
    Electronic Resource
    Electronic Resource
    Design sensitivity analysis with isoparametric shell elements (1993)
    Springer
    Structural and multidisciplinary optimization 5 (1993), S. 152-158 
    Details
    ISSN: 1615-1488
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract This paper deals with design sensitivity calculation by the direct differentiation method for isoparametric curved shell elements. Sensitivity parameters include geometric variables which influence the size and the shape of a structure, as well as the shell thickness. The influence of design variables, therefore, may be separated into two distinct contributions. The parametric mapping within an element, as well as the influence of geometric variables on the orientation of an element in space, is accounted for by the sensitivity calculation of geometric variables, and efficient formulations of sensitivity calculation are derived for the element stiffness, the geometric stiffness and the mass matrices. The methods presented here are applied to the sensitivity calculations of displacement, stress, buckling stress and natural frequency of typical basic examples such as a square plate and a cylindrical shell. The numerical results are compared with the theoretical solutions and finite difference values.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01743351
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  • 4
    Electronic Resource
    Electronic Resource
    An improved approximation for stress constraints in plate structures (1993)
    Springer
    Structural and multidisciplinary optimization 6 (1993), S. 1-6 
    Details
    ISSN: 1615-1488
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: Abstract An improved approximation for stresses (and strains) in plate structures is presented. This approximation is highly accurate because it is based on approximations of the element forces, which are more invariant than the element stresses and strains, and because it captures the nonlinearity in the stress recovery calculations. Both sizing and shape design problems are used as examples to show the increased accuracy and robustness of this approximation function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01743168
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  • 5
    Electronic Resource
    Electronic Resource
    Optimum design of composite structures (1989)
    Chichester [u.a.] : Wiley-Blackwell
    International Journal for Numerical Methods in Engineering 27 (1989), S. 437-448 
    Details
    ISSN: 0029-5981
    Keywords: Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mathematics , Technology
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/nme.1620270214
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  • 6
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    CONMIN- CONSTRAINED FUNCTION MINIMIZATION (1994)
    In:  Other Sources
    Details
    Publication Date: 2011-08-24
    Description: In many mathematical problems, it is necessary to determine the minimum and maximum of a function of several variables, limited by various linear and nonlinear inequality constraints. It is seldom possible, in practical applications, to solve these problems directly. In most cases, an iterative method must be used to numerically obtain a solution. The CONMIN program was developed to numerically perform the minimization of a multi-variable function subject to a set of inequality constraints. The function need not be a simple analytical equation; it may be any function which can be numerically evaluated. The basic analytic technique used by CONMIN is to minimize the function until one or more of the constraints become active. The minimization process then continues by following the constraint boundaries in a direction such that the value of the function continues to decrease. When a point is reached where no further decrease in the function can be obtained, the process is terminated. Function maximization may be achieved by minimizing the negative of the function. This program is written in FORTRAN IV for batch execution and has been implemented on a CDC 6000 series computer with a central memory requirement of approximately 43K (octal) of 60 bit words. The CONMIN program was originally developed in 1973 and last updated in 1978.
    Keywords: NUMERICAL ANALYSIS
    Type: ARC-10836
    Format: text
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  • 7
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    General purpose optimization software for engineering design (1990)
    In:  CASI
    Details
    Publication Date: 2004-12-04
    Description: The author has developed several general purpose optimization programs over the past twenty years. The earlier programs were developed as research codes and served that purpose reasonably well. However, in taking the formal step from research to industrial application programs, several important lessons have been learned. Among these are the importance of clear documentation, immediate user support, and consistent maintenance. Most important has been the issue of providing software that gives a good, or at least acceptable, design at minimum computational cost. Here, the basic issues developing optimization software for industrial applications are outlined and issues of convergence rate, reliability, and relative minima are discussed. Considerable feedback has been received from users, and new software is being developed to respond to identified needs. The basic capabilities of this software are outlined. A major motivation for the development of commercial grade software is ease of use and flexibility, and these issues are discussed with reference to general multidisciplinary applications. It is concluded that design productivity can be significantly enhanced by the more widespread use of optimization as an everyday design tool.
    Keywords: COMPUTER PROGRAMMING AND SOFTWARE
    Type: NASA. Langley Research Center, The Third Air Force(NASA Symposium on Recent Advances in Multidisciplinary Analysis and Optimization; p 185-190
    Format: text
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  • 8
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    Efficient calculation of optimum design sensitivity (1985)
    In:  Other Sources
    Details
    Publication Date: 2011-08-19
    Keywords: STRUCTURAL MECHANICS
    Type: AIAA Journal (ISSN 0001-1452); 23; 1798-180
    Format: text
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  • 9
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    Structural optimization by methods of feasible directions. (1973)
    In:  Other Sources
    Details
    Publication Date: 2011-08-16
    Description: A general design algorithm based on methods of feasible directions is presented. Zoutendijk's method of feasible directions is first presented as applied to structural design. This method is modified to improve numerical stability of the design process and is then further modified to deal efficiently with infeasible designs. The algorithm requires the analytic gradient of the objective function and the constraint functions which are active at a given stage in the design process. Gradient information is not required for nonactive constraints. Complex constraint functions may be ignored in the initial design stages because violation of these constraints is efficiently overcome later in the design process. The algorithm is demonstrated with elastic design of redundant trusses.
    Keywords: STRUCTURAL MECHANICS
    Format: text
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  • 10
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    The auxiliary problem for feasible directions (1975)
    In:  Other Sources
    Details
    Publication Date: 2011-08-16
    Description: The present work compares the computational efficiency of two means of determining a direction vector S at constraint boundaries and demonstrates the advantages of using the alternative that formulates the S-determination subproblem with a single quadratic constraint, which in turn can be cast as a special linear problem and solved directly.
    Keywords: NUMERICAL ANALYSIS
    Type: AIAA Journal; 13; May 1975
    Format: text
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