摘要:

AbstractA review is given of some mathematical programming methods suitable for optimization of structures needing matrix methods for analysis. An application is presented for elastic flat grillages made of straight orthogonal beams normally loaded. Empirical relationships are used to relate beam section properties so that each beam element has only one design variable. Optimization results are obtained by methods of stress‐ratio, linear programming‐cutting plane and usable‐feasible gradient directions. A comparison of the efficiency of these methods is given for the grillage designs which are shown to have non‐convex stress constraints and numerous relative optima. Instances are given of non‐fully stressed global optima and fully stressed designs which are not local optima for cases with only stress constraints. Discussions include locating the global optima for grillage designs and extensions of the methods presented to other structural design

ISSN:0029-5981    

DOI:10.1002/nme.1620010402

出版商:John Wiley&Sons, Ltd    

年代:1969

数据来源: WILEY

摘要:

AbstractThe paper presents a method for reducing the size of a vibration analysis by generating an inertia matrix referred to a limited set of ‘master’ vibrational freedoms. In designing a computer program to perform this mass condensation process, the emphasis has been on providing a two way interface between structural analysis and vibration analysis programs. The transformation from the full set of degrees of freedom to the master set makes extensive vibration calculations economically feasible giving solutions in terms of the amplitudes of the master freedoms. However, by reversing the transformation after completion of a vibration analysis, it is possible to restore the full set of freedoms, allowing automatic plotting of mode shapes in full detail, and re‐entry to the structural analysis program for the purpose of computing dynamic stresses.A worked example is given. This is a realistic machine tool structure rather than the simple plates or beams which are usually used for illustration purposes. Natural frequencies and mode shapes, calculated with various degrees of condensation, are compared with those obtained by using all possible freedoms. A comparison is also made with an intuitive selection of ‘lumped

ISSN:0029-5981    

DOI:10.1002/nme.1620010403

出版商:John Wiley&Sons, Ltd    

年代:1969

数据来源: WILEY

摘要:

AbstractThe application of non‐linear programming methods for the optimum design of statically indeterminate structures is discussed, with special emphasis on the design of elastic grillages loaded laterally and in plane. Some features of SUMT (sequential unconstrained minimization technique) are demonstrated by means of numerous examples of varying complexity. The Variable Metric method of search is discussed and compared to Powell's Direct Method. It is shown that non‐convex sets of design variables are often encountered in structural problems of the grillage type. SUMT may still be used, but the choice of starting value and initial response factor decisively influences the chance of finding the global optimum.It is demonstrated that a fully stressed design may not necessarily correspond to the minimum weight design. Optimum design of grillages which are simultaneously subjected to lateral and in‐plane loads may be performed efficiently by means of non‐linear prog

ISSN:0029-5981    

DOI:10.1002/nme.1620010404

出版商:John Wiley&Sons, Ltd    

年代:1969

数据来源: WILEY

摘要:

AbstractA completely numerical method for steady state linear viscoelastic stress analysis is presented by means of the finite element approach. Numerical representations of the measured viscoelastic constitutive relations are used. This method is developed to obtain steady state solutions to mixed boundary value problems in which the character of the boundary conditions at a point changes with time. Such problems cannot be handled by direct application of the correspondence theorem. A numerical example of viscoelastic sheet rolling is presented along with an experimental verification of the solution by photo‐viscoelastic observation

ISSN:0029-5981    

DOI:10.1002/nme.1620010405

出版商:John Wiley&Sons, Ltd    

年代:1969

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620010406

出版商:John Wiley&Sons, Ltd    

年代:1969

数据来源: WILEY

ISSN:0029-5981    

DOI:10.1002/nme.1620010401

出版商:John Wiley&Sons, Ltd    

年代:1969

数据来源: WILEY