The Optimization Of Truss-Like Structures By Sequence Linear Programming

With the development of science and people’s life demand, the modernconstruction industry is constantly evolving. On condition of meeting the mechanicalconditions and certain conditions of use, how to build structures reasonably andeconomically become a hot one in the field of structural design. Topologyoptimization of truss-like materials by mathematical programming methods is thecore theory of this paper.At present the studies about the topology optimization of continuum structureswith displacement constraints and stress constraints is numerous, but there are alsosome problems such as the applicability of the law of the fully-stressed criterion isnot extensive、 numerical instability in the topology optimization such ascheckerboard pattern is common and it’s hard to establish a model to expressexplicitly function of displacement constraints related to design variables.Mathematical solution of the topology optimization of truss-like materialsunder multiple load cases with stress constraints was studied. The optimizedstructure was non-uniform anisotropic continuum which was formed bycontinuously distributed truss-like materials. Structure was analyzed by the finiteelement method. The densities and directions of members of truss-like material atnodes were taken as design variables. The materials distribution in the elements wereinterpolated according to the material properties at the nodes belong the elements.Topology optimization method of truss-like structures by sequence linearprogramming was established. Compared with the standard method, the solution ismore general. The elasticity matrix, stiffness matrix and their sensitivities werededuced. The linear expansion expressions of material volume as objective, stressconstraints and displacement constraints were deduced. Linear programmingexpression of the topology optimization was established. The results can be used asthe base to form the truss structure furthermore. The model of truss-like structure established can effectively avoid the checkerboard pattern in the topologyoptimization and express function of displacement constraints related to designvariables reasonably. Mathematic program method expand the range its beingapplicable...