Static Topology Optimization For Plate And Shell Structure With Design Variable Controlling Elements

As rare yet important load bearing structural form in the project, the topologyoptimization design of plate and shell structure is a research hotspot in currenttopology optimization field. Although the study of continuum structure topologyoptimization has been a very depth development demostic and overseas, All is oneunit corresponding to a design variables. This delays the development of structuraltopology optimization in two aspects:(1)the elements ascertained firstly having thesame topology parameters can not be simplified to one topology variablecontrolling.(2) Can’t meet the practical requirements that certain unit having the sametopological variable are controlled by one design variable. Consequently, based onICM method, the optimal topologies of the plate and shell structure with each designvariable controlling multiple elements under static loads are studied in this paper.(1) The implementation process of design variable controlling elements isintroduce in detail. Based on ICM method, an approximately explicit topologicaloptimization model of plate and shell structure with each design variable controllingmultiple elements is established to minimize the weight with displacement and stressconstraints. The model is solved by SQP (sequential quadratic programming)algorithm using exact dual mapping and the optimal topology is finally obtained.This can reduce the number of design variables and improve the efficiency of thesolution. The dynamic inversion strategy makes the topology structure afterinversion more reasonable.(2) The design thought of each design variable controlling multiple elements isapplied in topological optimization of plate and shell structure with displacementconstraints. An explicit formulation of displacement constraint is obtained usingMohr’s theorem. Analyse the plate structure model with different displacementconstraints and the shell structure model under different boundary conditions.Examples indicate that compared to the thought of each design variable controllingone element, the thought of each design variable controlling multiple elements notonly can improve the computational efficiency greatly, but aslo meet the engineeringrequirement of controlling structure topology optimization geometries artificially.(3) The stress constraints is transformed into distortional strain energyconstraint according to distortion energy theory, to achieve stress constraints globalization which is used to slove the topology optimization of plate and shellstructure with stress constraints, this can reduce the number of stress constraints.Analyse the plate structure and the shell structure model with different stressconstraints under different boundary conditions. Examples indicate that the designthought of design variable controlling elements is practical and feasible, and can beobtained reasonable topology results and short compution time. It provides supportfor large-scale model calculation in engineering practice.(4) MSC/Patran&Nastran software is taken as secondary developmentplatform to realize the algorithm in this dissertation. It is implemented by PCLlanguage. The software has friendly user interface and link Matlab software. It canbe used to carried out optimization calculations. Optimization method is applied toengineering practice by software secondary development.