Theory Method And Secondly Development Of Dynamic Topology Optimization Design For Plate Structure

Topology optimization to continuum structure is generally recognized as themost challenging in the field of structural optimization. Compared to the sizeoptimization or shape optimization, topology optimization has a significant impact onimproving statics and dynamics performance of the structure. At present, manystudies have been made in the field of statics topology optimization. Compared withstatics topology optimization, it is difficult to establish the mathematical optimizationmodel, solve the sensitivity analysis and numerical instability. On the other hand, forshell structure, there are still a lot of complex technical problems on the load casesand special materials, so less dynamic topology optimization for shell structure werestudied. As a result, the theoretical research of dynamics of topology optimization forshell has a very important significance and engineering application prospects.This paper is based on ICM (independent, continuous, mapping) topologyoptimization method. It aims at minimization of structure weight subjected todynamic parameters constraint, and studies on the dynamic characteristics and thedynamic response problem of topology optimization. The complex problems, such ascomposite materials, fluid-structure interaction and the numerical instabilityphenomenon are researched. The main contents of this paper can be summarized asfollows:(1) Starting from the basic concepts of ICM method, by introduction of stepfunction and polishing function, this paper expounds "independent","continuous"which is the essence of ICM method. Through the in-depth study on the polishfunction and filtering function, this paper researches the process of “continuous”–“discrete”–“continuous” mapping, and analyzes the recognition function of the filterfunction in the process of solving optimal model.(2) Based on the ICM method, the optimization model of minimization shellstructure weight subjected to frequency constraints is established. It analysesmathematical characteristic equation of free vibration, and according to themathematical property, the local modal numerical instability problem is studied. Thesequence of the approximate optimization is applied to make constraint equationsexplicit. Then, the optimization model is divided into two layers which are inside andoutside iteration. In order to improve the solution efficiency, the inner mathematicalmodel is transformed based on the theory of dual programming.(3) The modal analysis with fluid-structure interaction is studied. The forcedvibration differential equation is transformed into the modal characteristic equation byvirtual quality method. The mathematical model of minimization of shell structureweight subject to frequency constraints with FSI is established, and is solved by the method of solving the dynamic characteristics topology optimization problem.(4) The new logarithmic filter function is constructed, which is applied to dealwith the model minimization of structure weight subjected to response amplitude ofthe harmonic excitation based on the ICM method. By the sequential approximationmethod and the design sensitivity analysis, the mathematical optimization model istransformed into explicit equation, which is solved by the dual quadraticprogramming method.(5) Dynamic topology optimization problem with anisotropic materials is studied.ICM method is expanded to the field of anisotropic material. Then topologyoptimization of shell structures of different layer angle are discussed in more detail.On the other hand, the laminated material is applied and the topology optimizationdesign and the non-design area can be selected. So that the limited shells, such ascontainers could take advantage of the research achievements of topologyoptimization of dynamic characteristics.(6) The optimal approach and its algorithm in the above have been implementedby the development platform of MSC.Patran and MSC.Nastran software. ThePCL(Patran Command Lauguage) is applied to add new menus and window in thebase of MSC.Patran, and implement the function of data exchange and solution of theoptimization model...