The Computational Efficient Continuum Topology Optimization Methods That Considering Manufacturability And Safe Robustness

In industrial productions,designing plays a vital role in achieving the goals of lightweight,high performance,or special mechanical properties.In the early days,the products are mainly designed based on experience,which often requires a very long period and the performance of the product is closely related to the designer's experience and ability.Nowadays,the rapid development of structural optimization methods provides theoretical guidance for designers.Due to the high design freedoms and the excellent engineering application value,topology optimization technology is favored by designers.At present,in the field of topology optimization,more and more attention has been paid to the manufacturability and the applicability of topology optimization results.This work is dedicated to promoting topology optimization to engineering applications and mainly addresses the grey element,jagged boundary,low computational efficiency at large-scale models,and poor robustness for deterministic structures in existing topology optimization methods.A series of numerical examples are tested to verify the effectiveness of the proposed methods.The specific research contents of this paper are as follows:(1)The topology optimization method based on an adaptive mesh adjustment algorithm is proposed.Aiming at the problems of blurred boundary and grey elements existing in the topology optimization results,a criterion is proposed to instruct the deformation of finite elements by shifting element nodes.To smooth the structural boundary,the element is inclined to the structural boundary.To reduce the proportion of grey elements,the element in the transition along the boundary is refined;on the contrary,the pure solid or void element is coarsened.Several 2D and 3D numerical examples indicate the effectiveness of the proposed method.Besides,a design process based on the presented method is proposed to make the optimum solutions be fabricated conveniently and accurately by linking it with the 3D design software,ie,Solid Works,which is also demonstrated in the numerical examples.(2)A computationally efficient multi-resolution topology optimization approach(MTOP)is proposed to handle the high-resolution or large-scale models.Based on the Solid Isotropic Material with Penalization(SIMP)method,the proposed approach employs the coarser mesh to perform the analysis,the sub-parts partitioned from finite elements to describe the material distribution and the nodal design variables to perform the optimization.To model the material discontinuities within one finite element,the extended finite element method(XFEM)is introduced.Based on the framework of XFEM,the finer sub-parts are endowed with individual material properties and shape functions.To improve the accuracy of the optimization results and yield discrete topology solutions,a modified sensitivity filter scheme is presented to eliminate grey elements.Typical 2D and 3D examples are carried out to verify that the proposed method yields high-resolution designs that preserve the topological complexity using fewer computational cost.(3)Based on the proposed multi-resolution framework(MTOP),the computationally efficient topology optimization method is proposed to minimize the maximum von Mises stress.In this work,the stress of each sub-part is calculated through a large number of Gauss integration points,which describes the stress distribution more accurately than traditional methods.The global stress is approximated by the P-norm method.The pq approach and the modified sensitivity filter are combined to solve the stress singularity problem.Finally,several numerical examples justify that the X-SIMP method generates topology solutions with lower stress using fewer computational cost.(4)Based on the proposed multi-resolution framework(MTOP),an efficient failsafe topology optimization approach is established.The fail-safe topology optimization is valuable to keep the optimized structures operable under a damaged state,whereas the expensive computational efforts at solving thousands of equilibrium equation extremely confine its development in industrial applications.To provide the designer with highperformance fail-safe structures whilst keeping the computational efforts tractable,a series of failure cases are established on finer material grids and are modeled by the removal of material stiffness with a fixed shape.The damaged compliance of the worst failure case is set as the optimization objective,and the KS function is adopted to approximate the non-differentiable max-operator.Several numerical examples demonstrate that the developed methodology is respectively 3 times and one order of magnitude faster than the traditional fail-safe topology optimization for 2D and 3D problems,at the same time maintaining their competitive mechanical properties.(5)A novel fail-safe topology optimization method with the guidance of von Mises stress is proposed.Due to the location of the damage is unknown in prior,a high number of failure scenarios have to be calculated when considering fail-safe requirement in topology optimization.In this article,we introduce the von Mises stress into fail-safe topology optimization to eliminate those unnecessary failure cases.First,several patches with predefined shapes are used to simulate the material failure.Then,the material properties of damaged models are interpolated by von Mises stress to construct the wellposed optimization model.The damaged compliance of the worst failure case is set as the optimization objective,and the KS function is adopted to approximate the nondifferentiable max-operator.To suppress the highly nonlinear stress behavior and the phenomenon of optimization oscillation,an extended variable update scheme within the framework of the Optimality Criteria(OC)method is developed.Finally,representative benchmark examples show the effectiveness of the presented method.