Eigen-solution for large structural systems with substructures

Civil and structural engineering Akay, H U 'Dynamic large deflection analysis of plates using mixed finite elements' Comput & Struct. Vol 11 No 1 - 2 (February 1980) pp 1-11 A four-node isoparametric mixed quadrilateral element is developed for large deflection dynamic analysis of plates. Dynamic yon Karman plate equations are modified to include the effect of transverse shear deformations as in Reissner plate theory. Finite element equations of motion are obtained via a mixed-Galerkin approach with three moment and three displacement components as dependent variables. Resulting nonlinear time dependent equations are solved by using Newmark's step-by-step direct integration algorithm in conjunction with Picard type successive iterations within each time step. The efficiency and accuracy of the proposed algorithm are demonstrated with numerical results. Anand, S C, and Shaw, R H 'Mesh-refinement and substructuring technique in elasticplastic finite element analysis' Comput. & Struct. Vol 11 No 1 - 2 (February 1980) pp 13-21 Although substructuring techniques and finite element mesh-grading schemes have been utilized independently in computer structural analysis within the elastic range, there exists no evidence in the literature of their simultaneous use, particularly in the inelastic range. A joint application of these two techniques using elasticplastic finite element analysis is presented in this paper. It is shown that the two can be successfully applied together, and may even lead to some savings in computational effort. Arora, Jasbir S, and Nguyen, D T 'Eigensolution for large structural systems with substructures' Int. J. for Numericol Methods in Eng. Vol 15 No 3, (March 1980) pp 333-341 A method for calculating natural frequencies and mode shapes of large structural systems with substructures and the subspace iteration procedure is developed. The method uses only the substructural stiffness matrices and the mass matrix for each element of the system. Efficiency of the method is improved when the mass matrix for the entire structure is computed and stored in core, although this is not necessary. No approximating assumptions are made in this method. Cantu, E and Cinquini, C 'lterative solutions for problems of optimal elastic design' Comput. Methods in App. Mech. and Eng. Vol 20 No 3 (December 1979) pp 257-266 An iteractive procedure is presented for the optimal design of one-dimensional structures with prescribed linear or rotational displacement at a given point. With reference to continuous beams the elastic discritized problem is formulated by using the finite element technique; the optimality condition is obtained by the variational method.

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Chyutin, M and Mittwoch, D Z 'Optimal allocation of facilities in high-rise buildings', Build. and Env. Vol 14 (1979) pp 235-239 In-and outing human traffic is one of the major considerations in designing high-rise buildings and their elevator systems. A method of allocating activities on the various floors, so as to minimize the total distance travelled within the building on entering or leaving activity areas, is presented in this paper. The model presented is a special form of the transportation problem and the proposed algorithm is applicable not only to the problem presented but may also offer an approach to the solution of other practical location problems. Fenves, S J 'Future directions of structural engineering applications' Comput. Struct. Vol 10 No 1/2 (April 1979) pp 3 - 6 The achievements and shortcomings of present computer applications in structural engineering are first reviewed and critiqued, in order to serve as a basis for identifying future trends. Future directions of computer applications are discussed from the standpoint of the dual driving forces of needs and opportunities. Three basic groupings of needs are identified in terms of technical, organizational and psychological needs, and plausible trends in each area are outlined. The opportunities are presented in terms of forthcoming developments in hardware and software. The potential impact of software engineering tools and methods on orderly program development is emphasized. Fleury, C 'Structural weight optimization by dual methods of convex programming', Int. J. for Numericcl/ Methods in Eng. Vol 14 No 12 (1979) pp 1761-1783 The paper is mainly concerned with a new structural optimization method based upon the concept of duality in convex programming. This rigorous formulation permits justification of many intuitive procedures which are used in the classical optimality criteria approaches. Furthermore, it is claimed that the dual algorithms proposed in this paper do not suffer from the drawbacks inherent to the optimality criteria approach. The efficiency of the dual algorithms is shown with reference to some problems for which the classical methods do not lead to satisfactory results. Fleury, C 'An efficient optimality criteria approach to the minimum weight design of elastic structures' Comput. Struct. Vol 11 No 3 (March 1980) pp 163-173 The paper concerns the optimality criteria approach to the minimum weight design of elastic structures analyzed by finite elements. It is first shown that the classical methods apply the lagrangian multiplier technique to an explicit problem. The approach presented results from high quality, first order approximations of the displacement constraints and cruder, zero order approximations of stress constraints. A generalized

optimality criterion is then proposed as the explicit Kuhn-Tucker conditions of a first order approximate problem. Numerical applications illustrate the efficiency of the generalized and hybid optimality criteria. Gero, J S 'Computer aided design by optimization in architecture' Des. Stud. Vol 1 No 4 (1980) pp 227 230 The paper shows that optimization concepts are particularly useful in design because of their decision making abilities. In this they subsume evaluation or apprasial techniques. One approach based on dynamic programming is presented as being directly applicable in computer aided architectural design. The approach presented can encompass very large, complex problems, can handle multi-attribute objectives and multi-objective designs through the use of Pareto optimal concepts. Gero, J S and Kaneshalingam, K 'Truss design by topology optimization', 7th Australasian Conf. Mech. of Struct. ond Mat. University of Western Australia (1980) pp 116--123 A method for truss design in which the topology of statically determinate trusses can be freely manipulated and the design optimized for topology, geometry and discrete member sizes for a multi-attribute objective function whose attributes include weight, cost of members and cost of fabrication, is presented in this paper. Dynamic programming using the delayed decision technique is employed to carry out the discrete multi-attribute optimization. This approach has been embodied in a computer program and results for a particular case are presented. Gran, C S, and Yang, T Y 'Refined analysis of the seismic response of column-supported cooling tower' Comput. Struct. Vol 11 No 3 (March 1980) pp 225-231 A cooling tower in Paradise, Kentucky (Tennessee Valley Authority) is studied. Half of the shell is modelled using orthotropic quadrilateral flat plate elements. The supporting columns and top ring beam are modelled by beam finite elements. The time-history response is computed by modal superposition, using the North-South component of the 1940 El Centro earthquake. A response spectrum analysis is used to ascertain the maximum response of the first three eccentric modes with four percent of critical damping. Hoa, S V, and Sankar, S 'A computer program for automatic generation of stiffness and mass matrices in finite element analysis', Comput. & Struct. Vol 11 No 3 (March 1980) pp 147-161 A computer program to automatically generate the stiffness and mass matrices in finite element analysis is introduced. By using programs like this, researchers

c o m p u t e r - a i d e d design