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  • 1
    Electronic Resource
    Electronic Resource
    An efficient approximate analysis method based on an exact univariate model for the element loads (1991)
    Springer
    Structural and multidisciplinary optimization 3 (1991), S. 107-114 
    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 Approximate analysis modules for structural design are usually based on a linear Taylor expansion of the nodal displacements in terms of the reciprocals of the design variables. Direct approximations of the member forces have received lesser attention. This paper describes an approach for the direct calculation of the member forces in a truss as a function of the design variables. It is based on the exact expression of the member forces if only one design variable is allowed to vary at a time. In the case of an arbitrary move in the design space the method gives approximate results of a very good quality. This is obtained by enforcing zero order homogeneity of the element loads and by refining the results via a virtual work equation. The method is illustrated with numerical results on previously published test cases for elastic trusses. Preliminary results for an elastic frame are also presented. This new approximate force model is shown to yield excellent results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01743280
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  • 2
    Electronic Resource
    Electronic Resource
    Internal forces expressed as ratios of polynomials in the unimodal stiffnesses (1994)
    Springer
    Structural and multidisciplinary optimization 8 (1994), S. 24-32 
    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 analytical solution of the linear structural problem is applied to generate approximate analysis models. As the exact expression is too long to be employed efficiently, its construct is used to develop explicit models for the internal forces. Two alternatives are presented. In both cases the models are exact along all the univariate lines radiating from the current point. A first model is created by using subsets of the exact expression. Although this approach gives excellent results it is plagued by linear dependency problems in selecting appropriate subsets. A second model can be viewed as a ratio of two linear Taylor series. After enforcing scaling invariance this model is equally efficient. The two methods are visualized by numerical examples of truss and frame design.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01742929
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  • 3
    Electronic Resource
    Electronic Resource
    Optimal design of infinite repetitive structures (1999)
    Springer
    Structural and multidisciplinary optimization 18 (1999), S. 202-209 
    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 approach for designing optimal repetitive structures under arbitrary static loading is presented. It is shown that the analysis of such infinite structures can be reduced to the analysis of the repeating module under transformed loading and boundary conditions. Consequently, both the design parameters and the analysis variables constitute a relatively small set which facilitates the optimization process. The approach hinges on the representative cell method. It is based on formulating the analysis equations and the continuity conditions for a sequence of typical modules. Then, by means of the discrete Fourier transform this problem translates into a boundary value problem of a representative cell in transformed variables, which can be solved by any appropriate analytical or numerical method. The real structural response any-where in the structure is then obtained by the inverse transform. The sensitivities can also be calculated on the basis of the sensitivities of the representative cell. The method is illustrated by the design for minimum compliance with a volume constraint of an infinite plane truss. It is shown that by employing this analysis method within an optimal design scheme one can incorporate a reduced analysis problem in an intrinsically small design space.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01195995
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  • 4
    Electronic Resource
    Electronic Resource
    A family of homogeneous analysis models for the design of scalable structures (1990)
    Springer
    Structural and multidisciplinary optimization 2 (1990), S. 143-152 
    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 Research in optimum structural design has shown that mathematical programming techniques can be employed efficiently only in conjunction with explicit approximate constraints. In the course of time a well-established approximation for homogeneous functions (scalable structures) has emerged based on the linear Taylor expansion of the displacement functions in the compliance design space (Reciprocal approximation). It has been shown that the quality of this approximation is based on the property that homogeneity of the constraints is maintained and consequently the approximation is exact along the scaling line. The present paper presents a new family of approximations of homogenous functions which have the same properties as the Reciprocal approximation and which produce more accurate models in most of the tested cases. The approximations are obtained by mapping the direct linear Taylor expansion of the constraints unto a space spanned by intervening variables (original design variables to a powerm). Taking the envelope of these constraints along the scaling line yields a new family of approximations governed by the parameterm. It is shown that the Reciprocal approximation is a particular member of this family of approximations (m = −1). The new technique is illustrated with classical examples of truss optimization. An optimal plate design is also reported. A parametric study of the results for various values of the exponentm is presented. It is shown that for special values of the exponentm the new approximations usually yield better models than those based on the Reciprocal approximation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01836563
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  • 5
    Electronic Resource
    Electronic Resource
    Nth-order stiffness sensitivities in structural analysis (1993)
    Springer
    Structural and multidisciplinary optimization 5 (1993), S. 207-212 
    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 presents a general expression for theNth-order stiffness sensitivities in linear elastic frames. It is based on modelling the structure as being composed of unimodal elements. It is shown that the sensitivity of the structural response to the variation of the stiffness of an arbitrary component depends only on the corresponding elemental displacements. These are the nodal displacements due to nodal element loads applied to the structure at the end nodes of the considered element. Therefore, on the basis of one structural analysis we obtain the sensitivity of the structure to the variation of a given stiffness, to any order and for all loading conditions. Partial derivatives with respect to several element stiffnesses are obtained from the elemental displacements of the considered elements. The method is equally applicable to more general finite element models. It requires, however, the preliminary decomposition of the finite elements into their unimodal components.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01743580
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  • 6
    Electronic Resource
    Electronic Resource
    Shape estimation of distorted flexible structures (1996)
    Springer
    Structural and multidisciplinary optimization 12 (1996), S. 237-243 
    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 present work discusses the optimal placement of sensors in truss structures in order to obtain best possible information regarding the distortions of the structure. The estimation goal is to reconstruct the deformed shape of the structure, at the controlled degrees of freedom, from the sensor readings. A basic assumption is that the structure is subjected to a parametric disturbance field. We distinguish between disturbances which cause uniform or arbitrary distortions of the structure, and disturbances which cause structured distortions. Uniform distortions can be construed as white noise, that is, distortions which have no characteristics. Structured distortions are chromatic, they have some characteristics which can be helpful in estimating the shape. Although the disturbance in either case is random it is assumed that its magnitude is confined to a hyper sphere. The estimator is based on the least squares method, hence the estimated shape is the one with least RMS displacement for the given sensor readings. To evaluate the performance of each set of sensors a measure is derived based on the concept of the worst case distortion. The measure is the largest possible error between the estimated and the actual displacements, at the CDOF. For small number of sensors all possible arrangements can be generated and compared. Larger trusses with a moderate number of sensors generate prohibitively large number of possible configurations, hence heuristic search techniques are employed. The theory has been applied to 2D and 3D flexible trusses. Results show that for reasonable shape estimation a relatively large number of sensors is needed. It is also shown that when using sensors which measure mainly the distortions of the controlled degrees of freedom, significant improvements in the shape estimation can be obtained.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01197363
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  • 7
    Electronic Resource
    Electronic Resource
    Topological structural analysis (1997)
    Springer
    Structural and multidisciplinary optimization 13 (1997), S. 104-111 
    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 Topological structural analysis is a terminology proposed for studying the behaviour of structures when the constitutive law is reduced to a least formulation. In addition to the equilibrium and deformation compatibility equations we only require that the extensional and contractile strains correspond, respectivley, to tensile and compressive stresses, without further specifying the nature of the constitutive law. The only analysis parameter in these equations is the equilibrium matrix which incorporates pure topological information such as node positions and bar connectivities. It is shown that in a topological context the internal forces, which can be realized by a structure, are bounded by a convex combination of the internal forces of its embedded statically determinate substructures. It is also shown that this “structural” equilibrium space is nonconvex. Consequently, the internal forces are bounded, component by component, by the internal forces in the statically determinate solutions. Having established that the structural equilibrium space is a small subset of the equilibrium space it is shown that pure equilibrium solutions, such as are obtained in plastic analysis and design, are not always feasible. It is conjectured that topological design of structures may benefit from using topological analysis rather than a pure equilibrium analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01199228
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