Qixiang Qing

An efficient method for topology optimization of continuum structures in the presence of uncertainty in loading direction

This paper presents a simple yet efficient method for the topology optimization of continuum structures considering interval uncertainties in loading directions. Interval mathematics is employed to equivalently transform the uncertain topology optimization problem into a deterministic one with multiple load cases. An efficient soft-kill bi-directional evolutionary structural optimization (BESO) method is proposed to solve the problem, which only requires two finite element analyses per iteration for each external load with directional uncertainty regardless of the number of the multiple load cases. The presented algorithm leads to significant computational savings when compared with Monte Carlo-based optimization (MCBO) algorithms. A series of numerical examples including symmetric and nonsymmetric loading variations demonstrate the considerable improvement of computational efficiency of the proposed approach as well as the significance of including uncertainties in topology optimization when to design a structure. Optimums obtained from the proposed algorithm are verified by MCBO method.

A simple reliability-based topology optimization approach for continuum structures using a topology description function

The structural configuration obtained by deterministic topology optimization may represent a low reliability level and lead to a high failure rate. Therefore, it is necessary to take reliability into account for topology optimization. By integrating reliability analysis into topology optimization problems, a simple reliability-based topology optimization (RBTO) methodology for continuum structures is investigated in this article. The two-layer nesting involved in RBTO, which is time consuming, is decoupled by the use of a particular optimization procedure. A topology description function approach (TOTDF) and a first order reliability method are employed for topology optimization and reliability calculation, respectively. The problem of the non-smoothness inherent in TOTDF is dealt with using two different smoothed Heaviside functions and the corresponding topologies are compared. Numerical examples demonstrate the validity and efficiency of the proposed improved method. In-depth discussions are also presented on the influence of different structural reliability indices on the final layout.

Robust topology optimization for continuum structures with random loads

This paper aims to tackle the challenge topic of continuum structural layout in the presence of random loads and to develop an efficient robust method.,An innovative robust topology optimization approach for continuum structures with random applied loads is reported. Simultaneous minimization of the expectation and the variance of the structural compliance is performed. Uncertain load vectors are dealt with by using additional uncertain pseudo random load vectors. The sensitivity information of the robust objective function is obtained approximately by using the Taylor expansion technique. The design problem is solved using bi-directional evolutionary structural optimization method with the derived sensitivity numbers.,The numerical examples show the significant topological changes of the robust solutions compared with the equivalent deterministic solutions.,A simple yet efficient robust topology optimization approach for continuum structures with random applied loads is developed. The computational time scales linearly with the number of applied loads with uncertainty, which is very efficient when compared with Monte Carlo-based optimization method.

Hybrid Structural Reliability Analysis under Multisource Uncertainties Based on Universal Grey Numbers

Nondeterministic parameters of certain distribution are employed to model structural uncertainties, which are usually assumed as stochastic factors. However, model parameters may not be precisely represented due to some factors in engineering practices, such as lack of sufficient data, data with fuzziness, and unknown-but-bounded conditions. To this end, interval and fuzzy parameters are implemented and an efficient approach to structural reliability analysis with random-interval-fuzzy hybrid parameters is proposed in this study. Fuzzy parameters are first converted to equivalent random ones based on the equal entropy principle. 3σ criterion is then employed to transform the equivalent random and the original random parameters to interval variables. In doing this, the hybrid reliability problem is transformed into the one only with interval variables, in other words, nonprobabilistic reliability analysis problem. Nevertheless, the problem of interval extension existed in interval arithmetic, especially for the nonlinear systems. Therefore, universal grey mathematics, which can tackle the issue of interval extension, is employed to solve the nonprobabilistic reliability analysis problem. The results show that the proposed method can obtain more conservative results of the hybrid structural reliability.

An Efficient Topology Description Function Method Based on Modified Sigmoid Function

Optimal geometries extracted from traditional element-based topology optimization outcomes usually have zigzag boundaries, leading to being difficult to fabricate. In this study, a fairly accurate and efficient topology description function method (TDFM) for topology optimization of linear elastic structures is developed. By employing the modified sigmoid function, a simple yet efficient strategy is presented to tackle the computational difficulties because of the nonsmoothness of Heaviside function in topology optimization problem. The optimization problem is to minimize the structural compliance, with highest stiffness, while satisfying the volume constraint. The design problem is solved by a Sequential Linear Programming method. Convergent, crisp, and smooth final layouts are obtained, which can be fabricated without postprocessing, demonstrated by a series of numerical examples. Further, the proposed method has a rather higher accuracy and efficiency compared with traditional TDFM, when the classical topology optimization methods, such as bidirectional evolutionary structural optimization (BESO) and solid isotropic material with penalization (SIMP) method, are taken as benchmark.

A Novel Design Framework for Structures/Materials with Enhanced Mechanical Performance

Structure/material requires simultaneous consideration of both its design and manufacturing processes to dramatically enhance its manufacturability, assembly and maintainability. In this work, a novel design framework for structural/material with a desired mechanical performance and compelling topological design properties achieved using origami techniques is presented. The framework comprises four procedures, including topological design, unfold, reduction manufacturing, and fold. The topological design method, i.e., the solid isotropic material penalization (SIMP) method, serves to optimize the structure in order to achieve the preferred mechanical characteristics, and the origami technique is exploited to allow the structure to be rapidly and easily fabricated. Topological design and unfold procedures can be conveniently completed in a computer; then, reduction manufacturing, i.e., cutting, is performed to remove materials from the unfolded flat plate; the final structure is obtained by folding out the plate from the previous procedure. A series of cantilevers, consisting of origami parallel creases and Miura-ori (usually regarded as a metamaterial) and made of paperboard, are designed with the least weight and the required stiffness by using the proposed framework. The findings here furnish an alternative design framework for engineering structures that could be better than the 3D-printing technique, especially for large structures made of thin metal materials.

Theoretical prediction and crashworthiness optimization of multi-cell polygonal tubes

Multi-cell polygonal tubes are highly efficient energy absorbers and widely used in vehicle engineering. There is no doubt that the structure designers have strong interest to know which kind of multi-cell polygonal tube has the best crashworthiness. However, the comparative study on the crashworthiness of multi-cell polygonal tubes with different edges was quite few. In this paper, the multi-cell polygonal single and bitubular tubes were investigated using the numerical simulation and theoretical prediction methods. Theoretical expressions of the mean crushing forces of the multi-cell polygonal single and bitubular tubes with arbitrary edge were derived by employing the simplified super folding element theory. The theoretical predictions well coincided with the numerical results. Based on the theoretical and numerical results, it can be found that the multi-cell polygonal bitubular tube with 18 edges had the best energy absorption capacity. In order to further improve the crashworthiness of multi-cell polygonal tube, a metamodel-based multi-objective optimization method which jointly employed the finite element simulation, metamodelling method and non-dominated sorting genetic algorithm ver. II multi-objective optimization algorithm was developed. Based on this metamodel-based optimization method, the multi-cell polygonal bitubular tube with 18 edges was optimized. The theoretical prediction also had good agreement with the numerical simulation result for the optimal design. The optimal multi-cell polygonal tube not only had excellent energy absorption capacity but also had stable collapse mode.