Optimization Design And Application Of Thin-walled Structures Considering Manufacturing Constraints

Thin-walled structures can realize lightweight design because of the high stiffness-tomass ratio,which are widely applied in automotive,aerospace and other engineering fields.Thin-walled frame structure and shell-infill structure are two types of thin-walled structure.Thin-walled frame structures can be regarded as consisting of thin-walled parts by traditional manufacturing processes such as stamping and extrusion.Traditional manufacturing processes with simple technology and low cost are suitable for mass production,but a variety of geometric requirements need to be considered.The shell-infill structure is a thin-walled structure filled with porous material,which has high stiffness,strength and stability.This structures are manufactured using additive manufacturing processes,which have few geometric requirements and provide the possibility for the manufacture of complex structures.Topology optimization is an efficient design method.For a given design domain,topology optimization method can design novel structures with high performances.However,the topological results are usually very complex.To make the optimized structure satisfy various manufacturing requirements,it is necessary to control the geometrical change of the topological results during the optimization procedure.In addition,the topological results obtained by the classical topology optimization method often take the form of a solid frame structure.There is an enormous gap between the topological results and thin-walled frame structures.Therefore,this paper firstly studies the topology optimization method with hollow and shell-infill features.Then,the thin-walled frame structure is designed by referring to the topological results considering the manufacturing process.These works carried out in this paper are given in detail below.Firstly,the topology optimization design method of hollow structure is studied.Combined with the advantages of the moving morphable component method to explicitly describe the topology structure,the topology description function with hollow features is constructed through the Boolean subtraction operation of the solid components.The topology optimization model with minimum compliance and volume constraints is established to design hollow structures.To improve the solution efficiency of the finite element model,the ersatz material model is adopted to solve the responses of the topological results.The sensitivities of the optimization model with respect to design variables are derived.The optimization problem is solved using the method of moving asymptotes.Numerical examples demonstrate that the proposed method can obtain hollow structures,whose stiffness is higher than that obtained by topology optimization of solid components.The effects of load conditions and initial structures on the topological results are also discussed.Then,the topology optimization design method for shell-infill structures with multiple filling materials is studied.The outer shell with uniform thickness and infill with multiple materials are constructed by a combination method of level set functions with the signed distance properties.Two optimization models are established,whose objective functions are compliance minimization and constraint functions are the volume fractions of different materials and total mass,respectively.The augmented Lagrange method is used to transform the constrained optimization problem into an unconstrained optimization problem.The size control function of the topological structure is defined based on the level set function.By adding penalty terms of size control function to the objective function,the topological results can satisfy the minimum size requirement.Because the topological structure is composed of multiple infill materials and outer shell material,the multi-resolution finite element method is used to solve the responses of the topological structure.The evolution velocities of the structural boundaries for the level set functions of the two optimization problems are obtained using the steepest descent method,and the upwind scheme of the difference method is adopted to update the level set functions iteratively.Numerical examples are used to verify that the proposed method can obtain the shell-infill structure with multiple infill materials,whose stiffness is higher than that of the shell-infill structure with single infill material.The effects of initial material layouts,constraint functions and material combinations on the topological results are also discussed.Finally,the thin-walled design method from the topological results considering stamping constraints is studied.First,the geometric properties of solid and thin-walled cross sections are derived.Then,to design complex thin-walled frame structures,classical topology optimization method is used to obtain the solid topological results.Afterward,the initial thin-walled cross section is designed according to the geometric properties of the solid cross section and the initial design requirements of the thin-walled cross section.Finally,considering the stamping process requirements,the thin-walled frame structure is designed with equivalent stiffness.The optimization model of the cross-sectional size and shape is established,which aims to minimize the structural mass with the stiffness and stamping requirements.This optimization model is solved using the sequential linear programming method.To facilitate the thin-walled design from the topological results,the design module of thin-walled cross sections and the optimization module of thin-walled frame structures are developed in independent industrial software Carframe.Numerical examples are used to verify the effectiveness of the proposed method to design the thin-walled frame structure by referring to the topological results.The thin-walled frame structure of automobile body is designed to promote the application of topology optimization method in thin-walled structure design.