Research On Theory Method And Software Development Of Stability Topology Optimization For Plate/Shell Structure

The topology optimization of continuum structure has advantages to reduce costs with little waste of material and determine the best layout of the material owing to the ability of finding the optimum transferring load path with the given constraints on the base structure.The plate/shell structure is widely applied in automobile,machinery,aerospace fields due to light weight,simple structure and the possibility of providing big useful space.However,the plate/shell structure is prone to instability,which is attributed to that the size of the thickness direction is far smaller than that of the length and width direction.Consequently,it is necessary to consider the stability for the topology optimization of plate/shell structure.This paper introduces the critical buckling load as the evaluation index of structural stability and researches the plate/shell topology optimization problem with pursuing the lightest structure based on the independent,continuous,mapping(ICM)method.The main works of this paper are summarized as follows:(1)Based on ICM method,the approximation properties and the performance of discretization of two filter functions,composite exponential function(CEF)and power function(PF),are studied in this paper.Two optimal solving strategies are proposed by introducing alternative and double filter functions to complete continuous double iterative process of topology variables.Then those optimal solving strategies are compared from the aspects of objective function,numbers of iterations and discretization of topology variables.(2)A stability topology optimization model of plate/shell is established,which subjects to critical buckling load constraint and takes the minimum structural mass as objective.The objective function is standardized based on the second-order Taylor expansion and the buckling constraint is approximately expressed as explicit function by taking advantages of the first-order Taylor expansion and sensitivity analysis.Therefore,the optimization model is translated into a quadratic programming.Finally the dual sequence quadratic programming(DSQP)algorithm is applied to solve the optimal model.The bisection inversion method is applied to reduce searching region of threshold space for realizing continuous approximation of the optimal threshold and the intelligent mapping of topology variables from “continuous” to “discrete”.The results of numerical examples demonstrate that the stability topology model of plate/shell is feasible and valid.(3)Both stability and dynamic characteristics of structure are integrated during the stage of optimal design.The topology optimization model with multi-properties constraints is established,with the minimum volume as objective function,the critical buckling load and nodal displacements as constraints.The displacement constraints are expressed as linear explicit function by using first-order Taylor expansion and Mohr theorem,and then topology optimization model is solved by converting into a quadratic programming model.In the numerical examples,the topology optimization models with multi-properties constraints and single-property constraint are compared from the aspects of objective function,perforamance of discretion and optimal topology.(4)The nature frequencies as the evaluation criteria of structural dynamic characteristics are considered into the stability topology optimization model with the minimum volume as objective.The frequencies constraints are written as linear explicit functions based on the linear Taylor expansion and Rayleigh quotient.And the standard dual optimization mathematical model is applied to solve the optimal model.The problems of local modal and modal exchange in dynamic topology optimization are discussed and analyzed.Numerical examples are given to analyze the influence of frequency constraint order,frequency constraint values and buckling constraint values on the optimization results.(5)According to the optimal approach and algorithm above,the related stability optimization modules are developed using PCL language on the software platform of MSC.Patran and Nastran.In addition,the new optimization menus and windows are added in the interface of MSC.Patran,which are convenient for users.