Multi-material Topology Optimization Research Articles

An Incremental Interpolation Scheme With Discrete Cosine Series Expansion for Multimaterial Topology Optimization

Abstract Topology optimization is a powerful tool for structural design, while its computational cost is quite high due to the large number of design variables, especially for multilateral systems. Herein, an incremental interpolation approach with discrete cosine series expansion (DCSE) is established for multilateral topology optimization. A step function with shape coefficients (i.e., ensuring that no extra variables are required as the number of materials increases) and the use of the DCSE together reduces the number of variables (e.g., from 8400 to 120 for the optimization of the clamped–clamped beam with four materials). Remarkably, the proposed approach can effectively bypass the checkerboard problem without using any filter. The enhanced computational efficiency (e.g., a ∼89.2% reduction in computation time from 439.1 s to 47.4 s) of the proposed approach is validated via both 2D and 3D numerical cases.

Multi-material topology optimization based on enhanced alternating active-phase algorithm

Multi-material topology optimization based on enhanced alternating active-phase algorithm

Transient heat conduction in multi-material topology optimization of thermoelastic structures involving dynamic constraints

This work presents a modified solid isotropic material with penalization (SIMP) for conducting dynamic-constrained multi-material topology optimization (MMTO) of thermoelastic structures subjected to transient thermal conduction. The novelty of this study is the multi-material optimization of instantaneous temperature conduction under specific frequency constraints, which has never been studied before. The proposed method has been developed for general models of multi-material interpolations such as thermal stiffness, heat capacity, and thermal stress coefficient. The temperature environment is formulated by applying prescribed mechanical and thermal loads that are exposed over a period of time. In this work, we focus on the objective of minimizing compliance in a transient heat conduction structure while simultaneously imposing constraints on the dynamics. With high temperatures, the stiffness of the optimization results decreases while stability is still guaranteed. The sensitivity of the objective function is subsequently calculated using the discretize-then-differentiate approach for the dynamic problem as well as the adjoint variable method. This study examines the impact of thermal fields and different time increments in conjunction with dynamic criteria. The outcomes of heat conduction result in notable alterations under identical dynamic constraint levels.

A multi-material topology optimization approach to hybrid material structures with gradient lattices

In this paper, we present a novel approach for designing hybrid material structures that incorporate solid, void, and spatially-varying lattices. This approach extends the recursively defined power-law type multi-material interpolation model by incorporating additional gradient material phases. Unlike conventional models, the new extended model considers the secondary ``solid'' material phase as a type of lattice, enabling adjustment of lattice geometry and mechanical behavior with gradient control variables such as density or size. By means of numerical homogenization and interpolation, we explicitly express the effective mechanical behavior of the gradient lattice in relation to the gradient control variable. This approach enhances design freedom by allowing for flexible control of individual material volumes, and also the lower and upper bounds of gradient variables. By using implicit geometrical modeling techniques, the resulting gradient control variable field can be interpreted to create spatially-varying and smoothly-connected lattices at any arbitrary resolution. The effectiveness and flexibility of the proposed approach have been demonstrated through a series of benchmark design tests considering various lattice material types.

A Novel Derivative Free Methodology for Multi-Material Topology Optimization Based on Projective Transformations and Boolean Operations

A Novel Derivative Free Methodology for Multi-Material Topology Optimization Based on Projective Transformations and Boolean Operations

Effects of Filtering and Current-Angle Adjustment on the Multi-Material Topology Optimization of a Three-Phase Stator

Effects of Filtering and Current-Angle Adjustment on the Multi-Material Topology Optimization of a Three-Phase Stator

Comprehensive multi-material topology optimization for stress-driven design with refined volume constraint subjected to harmonic force excitation

Comprehensive multi-material topology optimization for stress-driven design with refined volume constraint subjected to harmonic force excitation

Topology and orientation optimization of multi-material hinge-free composite compliant mechanisms under multiple design-dependent loadings

Compliant mechanisms with multiple input loads and output ports are commonly applied in micro-electromechanical systems (MEMS), while compliant mechanisms under design-dependent pressure loadings (such as pneumatic or hydraulic) can generate smooth and compatible deformations. Combining these two types of problems, we propose the design problem of compliant mechanisms under multiple design-dependent loadings. To potentially improve the structural performances, fiber-reinforced composite materials are introduced, and multi-material topology optimization and material orientation optimization are considered simultaneously, which enables the materials to be anisotropic and heterogeneous. Since compliant mechanisms utilize elastic deformation to transmit input forces or displacements to output forces or displacements, anisotropic and heterogeneous material can increase the freedoms in displacement and force transmissions compared to conventional homogeneous isotropic material. The topology optimization is implemented via an extended moving iso-surface threshold (MIST) method for multi-material, in which a novel element-based searching scheme is employed for tracking multiple fluid–structure interfaces. The orientation optimization is achieved via an analytical solution derived for fully anisotropic materials and multi-input-multi-output compliant mechanisms. Numerical examples are presented to show the validity of the present MIST method to design multi-material hinge-free compliant mechanisms under multiple design-dependent loadings.

FloatArch: A cable-supported, unreinforced, and re-assemblable 3D-printed concrete structure designed using multi-material topology optimization

3D concrete printing technology has advanced rapidly over the past decades, providing labor-saving benefits and the capability to achieve rapid construction of free-form structures. However, due to the involvement of robotic automation, the construction process in 3D concrete printing differs significantly from conventional concrete construction, especially in terms of concrete reinforcement. The current commonly used 3D printed concrete (3DPC) reinforcement techniques mainly include designing the 3DPC structure as predominantly compressed or prestressed components, or reinforcing it with auxiliary materials like steel rebars, fibers, or meshes. However, these methods either have limited application scenarios or do not fully utilize the mechanical performance of 3DPC materials. Building upon our previously proposed multi-material bi-directional evolutionary structural optimization (multi-material BESO) method, this paper introduces a new 3DPC structural design approach in which 3DPC components are predominantly subjected to compression, requiring no additional reinforcement but working together with tensioned steel cables to form an efficient composite structural system. We applied this method to the design and construction of an experimental prototype named “FloatArch”. Subsequent load tests and measurements confirmed the feasibility and efficiency of this 3DPC structure. We then designed and constructed the expanded structure “FloatSlab” to further demonstrate the general applicability of the proposed method. The features of prefabricated assembly, not requiring reinforcement or special equipment, and dry construction make this 3DPC structure easy to build and reassemble, providing new prospects for the sustainable use of 3DPC components. The generative design, construction, and validation of cable-supported structure prototypes presented in this paper demonstrate the immense potential of multi-material topology optimization technology for efficient 3DPC structural design, providing a new route to high-performance, innovative and sustainable structural design in additive manufacturing of concrete.

Multi-material topology optimization based on multiple simp of variable density method

Multi-material topology optimization based on multiple simp of variable density method

Design of the multiphase material structures with mass, stiffness, stress, and dynamic criteria via a modified ordered SIMP topology optimization

This paper, a multi-material topology optimization method (MMTO) is presented for two-dimensional structures using modified ordered solid isotropic material with penalization (SIMP) under multiple constraints such as mass, stiffness, frequency, and stress. The element density is obtained by a density filtering and the Heaviside approximation, which are combined to avoid gray elements and numerical issues of stress. Effective improvement of multiphase material topology optimization was performed including the criteria for stiffness, stress, and free vibration. P-norm stress aggregation is employed to calculate the maximum von Mises stress and sensitivity of von Mises stress is formulated by the adjoint method. The natural frequency and stress constraints are solved simultaneously to enhance the stability and reduce the stress concentration of the optimized structures, which are not much covered in the literature. The multi-mode phenomenon in the eigenfrequency problem is treated by the simply proposed technique. Results indicate that the multi-material designs with multi-constraints can be illustrated and optimized effectively. The optimized topologies, for stress minimization, indicate that the maximum stress can be significantly reduced compared with compliance minimization. The maximum von Mises stress of the topological results considering the maximum stiffness with natural frequency and mass constraints is higher than that maximum stiffness with only mass constraints, which indicates that the optimized structure created considering the eigenvalues is safer. The proposed approach can obtain a reasonable result that effectively controls the stress level and reduces the stress concentration at the high stress regions of multi-phase material structures with multi-constraints. Benchmark numerical examples are presented to confirm the effectiveness of the presented method.

Design of Viscoelastic Damped Plate Structures with a Multi-Material Topology Optimization Method

A viscoelastic damping layer attached to the plate structure can control vibrations but increases mass. Involving multiple viscoelastic materials, the contribution of different materials needs to be evaluated and allocated. In the paper, a topology optimization model is proposed to find distributions of different viscoelastic materials adopting a multi-material level set method, for maximizing single-order or multi-order modal loss factors. Limited by material volume fraction, the variational principle is applied to establish the velocity field, and the problem is solved by a gradient-based method. Numerical examples are performed to illustrate that loss factors of composite plate structures can be maximized with optimal distributions obtained from the multi-material level set method.

Probabilistic-Ellipsoid Hybrid Reliability Multi-Material Topology Optimization Method Based on Stress Constraint

Probabilistic-Ellipsoid Hybrid Reliability Multi-Material Topology Optimization Method Based on Stress Constraint

Multi-Material Topology Optimization for Spatial-Varying Porous Structures

Multi-Material Topology Optimization for Spatial-Varying Porous Structures

Multiresolution and multimaterial topology optimization of fail-safe structures under B-spline spaces

Multiresolution and multimaterial topology optimization of fail-safe structures under B-spline spaces

Orientation optimization via topological derivatives in combination with multi-material topology optimization based on extended level set method

This paper provides an orientation angle optimization method for the design of fiber-reinforced composite materials using topology optimization. The orientation angle optimization is based on a topological derivative, which measures the sensitivity of an objective function with respect to a topological change of anisotropic materials. The sensitivity is incorporated into a new gradient-based optimization algorithm. This method improves our ability to obtain better optimal candidates. We provide some numerical examples and verify the effectiveness of the proposed method.

Efficient multi-material topology optimization design with minimum compliance based on ResUNet involved generative adversarial network

Efficient multi-material topology optimization design with minimum compliance based on ResUNet involved generative adversarial network

Practical application of multi-material topology optimization to performance-based architectural design of an iconic building

With the rapid development of architectural design methods and structural analysis techniques, structural performance-based design approaches have become increasingly important in architectural design. Among these approaches, topology optimization is a significant design method. However, most existing topology optimization research and related applications are based on single-material topology optimization techniques, which have limitations when applied to the design of complex and challenging structures. Building upon our previously proposed multi-material bi-directional evolutionary structural optimization (multi-material BESO) method, this paper presents the approaches for achieving diverse and competitive structural designs and then presents a practical application of the multi-material BESO method to the structural design of the core structure of a long-cantilevered building project called “Xiong’an Wings”. After an evolutionary design process based on the multi-material BESO method, an efficient frame with lower overall material costs, better static and dynamic performance compared to the initial design by experienced engineers is achieved. As the first practical application of the multi-material BESO method to a large-scale architectural design, the example of the “Xiong’an Wings” building demonstrates the tremendous prospects for the application of multi-material topology optimization technology to the generative design of innovative and efficient building structures.

Topology optimization of compliant mechanisms under transient thermal conditions

This work considers multi-material topology optimization of compliant mechanisms under transient thermal and quasi-static mechanical conditions wherein thermally actuated devices are optimized for different operating conditions. The materials are modeled using finite strain thermo-hyperelasticity and a two way coupling between the energy balance and equilibrium equations is investigated. The design updates are generated from the gradient-based method of moving asymptotes optimizer and the sensitivities are computed using the time dependent adjoint sensitivity analysis. Results show the impact of designing for short versus long actuation times.

Dynamic-constrained multi-material topology optimization under heat flux and thermal–mechanical loading

In practice, the structures are often simultaneously related to thermal and mechanical loads, which can lead to stability failure. Improving the stability of the structures is needed to keep them safe. This study aims to optimize vibration capacity in a thermal environment by using an extended solid isotropic material with penalization (SIMP). The effects of thermal and mechanical loadings are considered simultaneously with dynamic constraints as a first effort that includes heat fluxes around boundaries. The incorporation of heat flux boundary conditions is explored in the multi-physics optimization instead of uniform heating using multi-materials. The results show that the distribution of materials changes significantly when thermal properties are changed. The adjoint method is used to analyze the sensitivity of objective functions, and the method of moving asymptotes (MMA) is employed to update new design variables. The effectiveness and reliability of the proposed method are verified by some examples.