Zeyu Deng¹, Yuan Liang^1,*, Gengdong Cheng¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.30, No.4, pp. 1-1, 2024, DOI:10.32604/icces.2024.012504

Abstract Compared to single-material optimization, topology optimization of multi-material structures offers a larger design space. It also requires efficient material selection methods to provide guidance for designers. The predominant methods are based on interpolation schemes, which introduce order-dependence issues during the optimization process. This means the sequence in which materials are arranged can significantly impact the optimization outcomes and may lead to notable issues with material gradation. This paper identifies the mathematical essence of multi-material topology optimization as a nonlinear multi-valued integer programming problem. In this paper, we propose a novel stochastic discrete steepest descent multi-valued More >

Jiaxiang Luo^1,2, Weien Zhou^2,3, Bingxiao Du^1,*, Daokui Li¹, Wen Yao^2,3,*

CMES-Computer Modeling in Engineering & Sciences, Vol.140, No.2, pp. 1919-1947, 2024, DOI:10.32604/cmes.2024.048118 - 20 May 2024

Abstract In recent years, there has been significant research on the application of deep learning (DL) in topology optimization (TO) to accelerate structural design. However, these methods have primarily focused on solving binary TO problems, and effective solutions for multi-material topology optimization (MMTO) which requires a lot of computing resources are still lacking. Therefore, this paper proposes the framework of multiphase topology optimization using deep learning to accelerate MMTO design. The framework employs convolutional neural network (CNN) to construct a surrogate model for solving MMTO, and the obtained surrogate model can rapidly generate multi-material structure topologies… More >

Zibin Mao¹, Qinghai Zhao^1,2,*, Liang Zhang¹

CMES-Computer Modeling in Engineering & Sciences, Vol.140, No.1, pp. 757-792, 2024, DOI:10.32604/cmes.2024.048016 - 16 April 2024

Abstract This paper proposes a multi-material topology optimization method based on the hybrid reliability of the probability-ellipsoid model with stress constraint for the stochastic uncertainty and epistemic uncertainty of mechanical loads in optimization design. The probabilistic model is combined with the ellipsoidal model to describe the uncertainty of mechanical loads. The topology optimization formula is combined with the ordered solid isotropic material with penalization (ordered-SIMP) multi-material interpolation model. The stresses of all elements are integrated into a global stress measurement that approximates the maximum stress using the normalized p-norm function. Furthermore, the sequential optimization and reliability assessment… More >

Chengwan Zhang¹, Kai Long^1,*, Zhuo Chen^1,2, Xiaoyu Yang¹, Feiyu Lu¹, Jinhua Zhang³, Zunyi Duan⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.138, No.1, pp. 369-390, 2024, DOI:10.32604/cmes.2023.029876 - 22 September 2023

Abstract This paper aims to propose a topology optimization method on generating porous structures comprising multiple materials. The mathematical optimization formulation is established under the constraints of individual volume fraction of constituent phase or total mass, as well as the local volume fraction of all phases. The original optimization problem with numerous constraints is converted into a box-constrained optimization problem by incorporating all constraints to the augmented Lagrangian function, avoiding the parameter dependence in the conventional aggregation process. Furthermore, the local volume percentage can be precisely satisfied. The effects including the global mass bound, the influence More >

Jun Yan^1,2, Qianqian Sui¹, Zhirui Fan¹, Zunyi Duan^3,*

CMES-Computer Modeling in Engineering & Sciences, Vol.130, No.2, pp. 967-986, 2022, DOI:10.32604/cmes.2022.017708 - 13 December 2021

Abstract This study establishes a multiscale and multi-material topology optimization model for thermoelastic lattice structures (TLSs) considering mechanical and thermal loading based on the Extended Multiscale Finite Element Method (EMsFEM). The corresponding multi-material and multiscale mathematical formulation have been established with minimizing strain energy and structural mass as the objective function and constraint, respectively. The Solid Isotropic Material with Penalization (SIMP) interpolation scheme has been adopted to realize micro-scale multi-material selection of truss microstructure. The modified volume preserving Heaviside function (VPHF) is utilized to obtain a clear 0/1 material of truss microstructure. Compared with the classic More >

MANIKANDAN.N^1,*, RAJESH.P.K¹

Journal of Polymer Materials, Vol.38, No.3-4, pp. 327-336, 2021, DOI:10.32381/JPM.2021.38.3-4.12

Abstract In this research, a new method to fabricate multi-material, multi-shape changing polymer composites is proposed. The method aims to reduce the number of thermomechanical programming steps involved in achieving shape change in a shape memory polymer (SMP) composite structure by including the programming steps directly into the printing process. After a single step of mechanical deformation and thermal loading, the SMP fibers can be activated sequentially to control the shape change. Composite strip samples were fabricated using a Stratasys Objet 260 multimaterial printer. Two polymer inks VeroPureWhite and Agilus30 were used as primary materials. The… More >

Baoshou Liu^1,2, Xiaolei Yan¹, Yangfan Li³, Shiwei Zhou⁴, Xiaodong Huang^3,*

CMES-Computer Modeling in Engineering & Sciences, Vol.128, No.2, pp. 523-540, 2021, DOI:10.32604/cmes.2021.017211 - 22 July 2021

Abstract This paper proposes a new element-based multi-material topology optimization algorithm using a single variable for minimizing compliance subject to a mass constraint. A single variable based on the normalized elemental density is used to overcome the occurrence of meaningless design variables and save computational cost. Different from the traditional material penalization scheme, the algorithm is established on the ordered ersatz material model, which linearly interpolates Young's modulus for relaxed design variables. To achieve a multi-material design, the multiple floating projection constraints are adopted to gradually push elemental design variables to multiple discrete values. For the More >

Xinqing Li¹, Qinghai Zhao^1,*, Hongxin Zhang¹, Tiezhu Zhang², Jianliang Chen¹

CMES-Computer Modeling in Engineering & Sciences, Vol.127, No.2, pp. 683-704, 2021, DOI:10.32604/cmes.2021.015685 - 19 April 2021

Abstract This paper presents a robust topology optimization design approach for multi-material functional graded structures under periodic constraint with load uncertainties. To characterize the random-field uncertainties with a reduced set of random variables, the Karhunen-Loève (K-L) expansion is adopted. The sparse grid numerical integration method is employed to transform the robust topology optimization into a weighted summation of series of deterministic topology optimization. Under dividing the design domain, the volume fraction of each preset gradient layer is extracted. Based on the ordered solid isotropic microstructure with penalization (Ordered-SIMP), a functionally graded multi-material interpolation model is formulated More >

Jinqing Zhao¹, Tianbao Ma^*

The International Conference on Computational & Experimental Engineering and Sciences, Vol.21, No.3, pp. 47-47, 2019, DOI:10.32604/icces.2019.06150

Abstract We describe a pseudo arc-length algorithm for numerical resolution of immiscible compressible multi-material flows with the Mie-Grüneisen type equation of state (EOS) governed by the quasi-conservative five-equation model. The governing equation is discretized in space uses the finite volume approach with a second-order accurate Godunov scheme. Time discretization is achieved using the strong stability-preserving high-order Runge-Kutta time discretization scheme. The five-equation model with the Mie-Grüneisen EOS is general enough to model materials with different equations of state and physical states. However, for long simulations, the interface of materials is indistinct because of numerical dissipation. The… More >

X. X. Cui¹, X. Zhang^1,2, K. Y. Sze³, X. Zhou⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.5, pp. 507-538, 2013, DOI:10.3970/cmes.2013.092.507

Abstract Based on the material point method (MPM), an alternating finite difference material point (AFDMP) method is proposed for modeling the 3D high explosive (HE) explosion and its interaction with structures nearby. The initiatory detonation and eventual fluid structure interaction (FSI) are simulated by the standard MPM. On the other hand, the finite difference method (FDM) is employed to simulate the dispersion of the detonation products into the surrounding air where the particles degenerate to marker points which track the moving interface between detonation products and air. The conversion between MPM and FDM is implemented by More >