Topology Optimization of Strength-Safe Continuum Structures Considering Random Damage

Spacecraft in the aerospace field and military equipment in the military field are at risk of being impacted by external objects,which can cause local damage to the structure.The randomness of local damage is a newchallenge for structural design,and it is essential to take random damage into account in the conceptual design phase for the purpose of improving structure’s resistance to external shocks.In this article,a random damaged structure is assumed to have damages of the same size and shape at random locations,and the random damage is considered as multiple damage conditions of the structure.In order to improve the randomness and comprehensiveness of the multiple damage conditions,the stacking strategy is used to generate the distribution of the damage area.Following this strategy,the topology optimization design of the random damaged structure,which is to minimize the weight of the structure with a constraint on the stress of the structure under multiple damage conditions,is formulated based on the independent continuousmapping(ICM)method.The dual sequence quadratic programming(DSQP)algorithm combined with the stress globalization method is adopted to solve the optimization problem.The numerical examples demonstrate the effectiveness and applicability of the proposed method in the topology optimization of strength-safe continuum structures.

Independent continuous mapping for topological optimization of frame structures

Based on the Independent Continuous Mapping method （ICM）, a topological optimization model with continuous topological variables is built by introducing three filter functions for element weight, element allowable stress and element stiffness, which transform the 0-1 type discrete topological variables into continuous topological variables between 0 and 1. Two methods for the filter functions are adopted to avoid the structural singularity and recover falsely deleted elements： the weak material element method and the tiny section element method. Three criteria （no structural singularity, no violated constraints and no change of structural weight） are introduced to judge iteration convergence. These criteria allow finding an appropriate threshold by adjusting a discount factor in the iteration procedure. To improve the efficiency, the original optimization model is transformed into a dual problem according to the dual theory and solved in its dual space. By using MSC/Nastran as the structural solver and MSC/Patran as the developing platform, a topological optimization software of frame structures is accomplished. Numerical examples show that the ICM method is very efficient for the topological optimization of frame structures.

Topology optimization of continuum structures considering damage based on independent continuous mapping method

A continuum topology optimization usually produces results similar to a skeleton structure. In addition, the material utilization in the optimized structure is greatly improved compared with the original structure. On the other hand, the redundancy of the structure is greatly reduced due to the removed material. A partial local failure in the optimized structure makes it more difficult for the entire structure to meet the strength/stiffness requirements. By using the independent continuous mapping (ICM) method, with minimal weight as the objective and both stress and displacement as the respective constraints, the continuum topology optimization models can be employed, which also consider damage. A dual-sequence quadratic programming (DSQP) algorithm is used to solve the topology optimization models. Numerical examples confirm the effectiveness and feasibility of the models. The results indicate that both a good load-path and weight reduction can be obtained. In addition, compared with the structure obtained using conventional topology optimization, redundancy is improved greatly, and the strength/stiffness requirements for the structure can be satisfied for each damage scenario. Furthermore, the results indicate that the strength/stiffness of the structure, after topology optimization, is slightly sensitive for local damage.

Fail-Safe Topology Optimization of Continuum Structures with Multiple Constraints Based on ICM Method

Traditional topology optimization methods may lead to a great reduction in the redundancy of the optimized structure due to unexpected material removal at the critical components.The local failure in critical components can instantly cause the overall failure in the structure.More and more scholars have taken the fail-safe design into consideration when conducting topology optimization.A lot of good designs have been obtained in their research,though limited regarding minimizing structural compliance(maximizing stiffness)with given amount of material.In terms of practical engineering applications considering fail-safe design,it is more meaningful to seek for the lightweight structure with enough stiffness to resist various component failures and/or to meet multiple design requirements,than the stiffest structure only.Thus,this paper presents a fail-safe topology optimization model for minimizing structural weight with respect to stress and displacement constraints.The optimization problem is solved by utilizing the independent continuous mapping(ICM)method combined with the dual sequence quadratic programming(DSQP)algorithm.Special treatments are applied to the constraints,including converting local stress constraints into a global structural strain energy constraint and expressing the displacement constraint explicitly with approximations.All of the constraints are nondimensionalized to avoid numerical instability caused by great differences in constraint magnitudes.The optimized results exhibit more complex topological configurations and higher redundancy to resist local failures than the traditional optimization designs.This paper also shows how to find the worst failure region,which can be a good reference for designers in engineering.