Structural Topology Optimization Method Research Articles

A new efficient parametric level set method based on radial basis function-finite difference for structural topology optimization

To overcome a significant challenge in traditional parameterized level set methods based on globally supported radial basis functions, we propose employing a local differentiation construction of radial basis functions using finite difference, a technique previously applied to solving partial differential equations but novel in the context of topology optimization. We present a novel parameterized level set method for structural topology optimization of compliance minimization and compliant mechanism, with the main aim of reducing computational costs associated with fully dense matrices when approximating systems with a large number of collocation points. The new scheme implemented with rectangular mesh elements and polygonal mesh generation accommodates both rectangular and complex design domains. Numerical results are provided to demonstrate the algorithm's effectiveness.

An adaptive phase-field method for structural topology optimization

In this work, we develop an adaptive algorithm for the efficient numerical solution of the minimum compliance problem in topology optimization. The algorithm employs the phase field approximation and continuous density field. The adaptive procedure is driven by two residual type a posteriori error estimators, one for the state variable and the other for the first-order optimality condition of the objective functional. The adaptive algorithm is provably convergent in the sense that the sequence of numerical approximations generated by the adaptive algorithm contains a subsequence convergent to a solution of the continuous first-order optimality system. We provide several numerical simulations to show the distinct features of the algorithm.

Designing piezoelectric stretcher through multiphysics topology for enhanced photodynamic therapy in cancer treatment

This study presents an advancement in Photodynamic Therapy (PDT) by introducing piezoelectric stretchers designed to enhance tissue surface characteristics. With a focus on mitigating the impact of irregular tissue surfaces on light distribution, we propose a structural topology optimization method to design a stretcher that utilizes the piezoelectric effect for precise tissue stretching. The aim is to achieve uniform laser irradiance across treated tissue, thereby maximizing therapy efficiency. Our approach involves the formulation of finite element models that consider the piezoelectric effect and the elastic response in a multiphysics framework. Mesh convergence tests were conducted to strike a balance between accuracy and computational efficiency in evaluating the designed piezoelectric stretcher. The investigation into the application of piezoelectric stretchers for enhancing laser irradiance on non-uniform tissue reveals significant improvements in surface uniformity with increasing electric potential. Notably, the disparity between regions of high laser focusing and defocusing decreases as the stretcher expands, achieved through the application of higher voltages. The observed enhancement from no expansion to full expansion is quantified at 31 %. The implementation of electrically driven piezoelectric tissue expansion results in a more uniform tissue surface, leading to an augmentation of laser irradiance. In the absence of expansion, distinct areas of laser focus and near-zero irradiance are noted. Conversely, an increased potential yields a predominantly even surface, with 100 % extension achieving commendable laser irradiance uniformity.

Metaheuristic aided structural topology optimization method for heat sink design with low electromagnetic interference

This study investigates the application of the Metaheuristic Aided Structural Topology Optimization (MASTO) method as a novel approach to address the multiphysics design challenge of creating a heat sink with both high heat conductivity and minimal Electromagnetic Interference (EMI). A distinctive 2D layout with elongated fins is examined for electromagnetic traits, highlighting resonance-related EMI concerns. MASTO proves to be a valuable tool for navigating the complex design space, yielding thoughtfully optimized solutions that harmonize efficient heat dissipation with effective EMI control. By merging simulation findings with practical observations, this study underscores the potential of the MASTO method in achieving effective designs for intricate multiphysics optimization problems. Specifically, the method's capacity to address the complex interplay of heat transfer with convection and the suppression of electromagnetic emissions is showcased. Moreover, the study demonstrates the feasibility of translating these solutions into tangible outcomes through manufacturing processes.

Reinforcement layout design for deep beams based on bi-objective topology optimization

Determining an effective and efficient reinforcement layout for reinforced concrete deep beams is still a challenging problem. This paper proposes a bi-objective evolutionary structural topology optimization method for the reinforcement layout design. Based on a discrete model for steel bars, the optimization aims to achieve a uniform stress distribution of steel rebars while promoting the peak rebar stress. A lexicographic method is used to solve the bi-objective optimization. Two numerical examples are presented to demonstrate the proposed algorithm's feasibility, stability and universal applicability. It is shown the reinforcement stresses in both tension and compression zones are more uniformly distributed and, on average, closer to the yield strength than those of the single-objective optimization. Compared with the design based on the conventional strut-and-tie method, the deep beams optimized by the proposed method use less reinforcement steel, provide a higher ultimate load capacity, and, more interestingly, fail in a ductile failure mode.

A node moving-based structural topology optimization method in the body-fitted mesh

The work presents a node-moving algorithm for topology optimization (NMTO) in the arbitrarily shaped design domain. Also, we further enhanced a body-fitted mesh generation algorithm to express smooth boundaries more efficiently. In each optimization iteration, a narrowband offset from the structural profile is established, based on which a signed-distance function is constructed to determine the node-moving direction. At the same time, the magnitude of node velocity is derived from the shape derivative of the objective function - the sum of mean compliance and mean curvature. After the signed-distance function is updated based on the new position of the nodes within the narrowband with the abovementioned velocity, boundaries implicitly represented by its zero-level contour are obtained naturally. Such a forward Euler updating scheme is much more efficient than the well-known upwind algorithm for the body-fitted mesh as it avoids the interpolation of triangular nodes to the rectangular nodes and a small time step. Compared with other methods, benchmark numerical examples demonstrate that the proposed method can produce elegant structures with smoother boundaries and better objective functions for optimization problems seeking maximal stiffness or displacement at a prescribed node. In addition, the proposed approach prevents, to a large extent, useless void parts from being included in the time-consuming finite element analysis.

Level set-based topology optimization for programmable acoustic structures

Controlling acoustic waves is essential in noise-reduction applications. Acoustic structures, which can efficiently manipulate acoustic waves based on their structural design, have been used to achieve the desired wave propagation behaviors. To meet various demands on sound propagation, it is crucial to design acoustic structures with multiple functionalities. In this research, we propose a level set-based topology optimization method for acoustic structures with desired acoustic performances that depend on their deformation. Firstly, we introduce a mathematical model that represents acoustic wave propagation based on the Helmholtz equation and the coordinate transformation. Next, we formulate the optimization problem based on the framework of a level set-based topology optimization method. A two-dimensional numerical example is provided to demonstrate the validity of the proposed method. As an example, we optimize a sound reflective structure with the desired acoustic responses that are dependent on the deformation of the optimized structure.

Topology Optimization Method for Microscale Structures Described with Integral Nonlocal Theory

Topology Optimization Method for Microscale Structures Described with Integral Nonlocal Theory

Integrated optimization of components’ layout and structural topology with considering the interface stress constraint

Structural designs in the engineering field commonly require the prior embedding of several fixed-shape components to satisfy desired performance or functional requirements. In the past few decades, topology optimization has been regarded as an effective approach to deal with the optimization problems of continuous structures embedded with multiple components. However, the interfaces between the host supporting structure and embedded components are assumed perfect-bonded, which may result that the optimal design occurs interface failure and structural damage under extreme or long-time service conditions. In this study, a new topology optimization method of structures with embedded components considering the tension/compression-asymmetric interface stress constraint is proposed under the solid isotropic material with penalization (SIMP) method framework. This proposed method optimizes simultaneously the topology of the host structure and the layout of embedded components. A new interpolation model is developed to determine interface layers between the host structure and embedded components. Then, interface stress constraints are derived and imposed on each element of interface layers. For relieving the computational burden caused by enormous stress constraints, the global p-norm stress aggregation method is adopted to quantify the peak stresses. Subsequently, the interface stress constraint is introduced into the integrated optimization of multi-component layout and structural topology, the objective function is structural compliance and constraint functions are composed of volume, non-overlapping and tension/compression-asymmetric interface stress constraints. The corresponding sensitivity analyses are computed by using the adjoint method. Several two-dimensional and three-dimensional numerical examples are provided to verify the effectiveness of the proposed method.

High-resolution topology optimization method of multi-morphology lattice structures based on three-dimensional convolutional neural networks (3D-CNN)

High-resolution topology optimization method of multi-morphology lattice structures based on three-dimensional convolutional neural networks (3D-CNN)

Isogeometric topology optimization for infill designs of porous structures with stress minimization in additive manufacturing

AbstractPorous structures by additive manufacturing have fascinating and compelling performance compared with solid structures. The stress‐related porous infill designs which could greatly mitigate the effects of the intrinsic high residual stress in additive manufacturing process have gained increasing attention. In the current work, we propose a promising Isogeometric Topology Optimization (ITO) method for porous infill structures with stress minimization to avoid the occurrence of stress concentrations in additive manufacturing. The IsoGeometric Analysis (IGA) and induced p‐norm aggregation are utilized to develop a stress‐minimization topology description model for infill design, which can remove the mesh dependency and offer benefits for improving numerical accuracy and convergence stability. We also introduced global volume constraints to easily control the usage of material and eliminate the over‐fine structures affecting the printing accuracy. Several numerical examples are performed to demonstrate the effectiveness and advantages of the proposed ITO method on porous infill designs with stress minimization. The laser powder bed fusion (LPBF) technique is employed to fabricate several prototypes, and the performance are evaluated by experiments. The advancements of our work are demonstrated effectively, which is adapted for additive manufacturing and practical application.

EMsFEM based concurrent topology optimization method for hierarchical structure with multiple substructures

An efficient concurrent topology optimization method based on the Extended Multiscale Finite Element Method (EMsFEM) is proposed to design the hierarchical structure with multiple substructures in this paper. Firstly, the mathematical description model for the topology of hierarchical structures and the interpolation model for material are established at both the macro and substructural levels. Then the concurrent topology optimization formulation for hierarchical structures is proposed based on EMsFEM. After that, the sensitivity analysis scheme of the objective function and constraint functions is given, based on which the Method of Moving Asymptotes (MMA) is employed to update design variables. The assumption of separation of length scales is not required in the proposed method, which avoids the disconnection between adjacent substructures. Besides, without limiting the topology and spatial distribution of substructures in advance, the concurrent topology optimization for hierarchical structures with multiple substructures can be realized using this method. The provided numerical examples verify the correctness and effectiveness of the proposed sensitivity analysis method as well as the feasibility, effectiveness and scalability of the proposed concurrent topology optimization method for hierarchical structures. Finally, the influence of the initial substructure configurations and the number of substructure types on the final configuration and mechanical performance of hierarchical structures are explored with a series of numerical examples.

Topology optimization of multi-material structures considering anisotropic yield strengths

Multi-material structures offer the superior performance and broader designable freedom, and have gained increasing interest benefitting from the advances in additive manufacturing (AM) technique. However, the effect of anisotropic yield strength of these AM-fabricated parts on topology optimization of multi-material structures has so far received little attention. In the current work, an anisotropic strength-based topology optimization method for multi-material structures is developed for maximizing strength performance under total mass constraint, which allows for the consideration of directional dependence and tension-compression asymmetry of yield strengths based on the Tsai-Wu yield criterion. Another challenge for multi-material structures design is that the possible permutations of numerous candidate materials are unlimited, it is impossible that all combinations of multiple candidate materials are tested for the optimal strength performance of multi-material structures. To solve this problem, we propose a preselection method for the inclusion or exclusion of candidate materials based on their elastic properties, yield strengths and densities before optimization. Afterwards, our topology optimization method can automatically find the optimal combination of volume fractions of different candidate materials. Several 2D and 3D numerical examples are investigated for minimizing the maximum of failure indexes of strength for fixed total mass. The advantages of multi-material structures are verified by comparing to single-material designs. The effectiveness of the preselection method of candidate materials is also verified.

Strength constrained topology optimization of hyperealstic structures with large deformation-induced frictionless contact

This paper developed a strength constrained topology optimization method for hyperelastic structures with large deformation-induced frictionless contact. The Neo-Hookean hyperelastic constitutive equation is adopted as the material model that incorporates both material and geometric nonlinearity. The large deforming contact is described by the node-to-segment algorithm. The topology optimization model is developed under the SIMP framework. Given the SIMP-related fictitious domain, we develop a nodal variable-based interpolation scheme to build smooth correlation between the contact force and nodal density variables, thus enabling the smooth transition and variation of contact conditions. Moreover, to guarantee the structure strength, local strain energy constraints are formulated and aggregated by the P-norm function. The details of sensitivity analysis are explicitly explained. At last, several benchmark examples are conducted that validate the proposed method.

A novel numerical manifold method and its application in parameterized LSM-based structural topology optimization

In this paper, a high-efficiency structural topology optimization framework based on combination of numerical manifold method (NMM) and parameterized level set method (PLSM) is established. The NMM uses two cover systems to discretize the model, which can accurately represent the complex boundary of the design domain. A new numerical manifold element has been derived for the application of NMM in PLSM-based optimization. To obtain enhanced accuracy for structural analysis, a multilevel subdivision technique for numerical manifold element generation is presented, and the related numerical integration scheme coupled with the interpolation point selection strategy is provided. For the proposed topology optimization, the new update method of element stiffness matrix is exclusively formulated as well as the calculation method of volume fraction. Some representative structural optimization problems demonstrate that the proposed structural topology optimization method is very effective for two-dimensional (2D) and three-dimensional (3D) structural topology optimization problems.

An enhanced proportional topology optimization with virtual elements: Formulation and numerical implementation

This paper presents an improved non-sensitivity structural topology optimization method incorporating virtual elements with unstructured polygonal meshes. Specifically, we employ the recently developed gradient-free proportional topology optimization (PTO) approach, for the first time, together with a new material distribution formula suitable for both minimum compliance and compliant mechanism problems. In order to improve performance, we integrate a linear virtual element method (VEM) module into the PTO algorithm. The linear VEM has a desirable characteristic: it does not require numerical integration and, more importantly, is less sensitive to small-edge elements, thus, significantly reducing computational time. Additionally, we utilize virtual elements with unstructured polygonal meshes inside PTO to suppress one-node connection instabilities. Furthermore, the Heaviside-type operator in the main PTO algorithm loop enhances the optimized results by encouraging the density variables to approach discrete (0/1) solutions more effectively. We demonstrate the performance of our developed method in terms of computational speed, diversity of applications, and improved black-and-white (0/1) structures through several benchmark examples of compliance and compliant mechanism designs.

A PID-optimality criteria method for structural topology optimization

A PID-optimality criteria method for structural topology optimization

Multi‐material topology optimization method for transient thermal structure with constraint on permissible temperatures

AbstractExcessive temperature may lead material to performance degradation, ablation, and phase change. Thus, controlling the maximum temperature of used material within a safe range is of great significance to the safe operation of thermal structures. In this article, a density‐based multi‐material topology optimization method for transient thermal structures is proposed, in which the maximal temperature for each material is controlled not greater than its permissible temperature. In this method, a projection algorithm based on the PDE (partial differential equation) filter and Heaviside projection is set up and used to identify the domains occupied by each material. The maximal temperature of each specific material occupying domain is approximately expressed by the condensed integrals in the time and space domains. The permissible temperature constraint is satisfied by controlling the condensed integrals not great than a specific threshold value (depending on the corresponding material's permissible temperature). Several examples illustrate that the permissible temperature plays an important role in the selection and the distribution scheme of the candidate materials for the design of multi‐material thermal structures. The proposed method can effectively control the maximal temperature of each material within its constraint range, and achieve the rational design for multi‐material thermal structures. In addition, different thermal loading time may also lead to different material selection of structure. This work has potential applications in the lightweight design of thermal insulation structures.

Fail-safe topology optimization for multiscale structures

This paper presents a novel fail-safe topology optimization method for multiscale structures. The partial damage of both macroscopic and microscopic scales is considered for structural design. To ensure precision, the effective elasticity tensor obtained by the homogenization method is fitted as a high-order polynomial function. Meanwhile, the simplified models of partially damaged truss-like microstructure are employed to reduce the computational cost and the difficulty of fitting. Moreover, Heaviside projection is applied to speed up the convergence and yield a relatively clear configuration. Three numerical examples are tested to demonstrate that the optimized multiscale structures successfully obtain comprehensive performances than optimized solid structures when appropriate microstructure configurations are chosen. Besides, multiscale structures are more self-supporting than solid structures and thus more suitable for additive manufacturing due to the large number of gray elements diffused.

A sequential mixed-integer programming method for concurrent optimization of core topology and face sheet thickness of a sandwich beam

A method is proposed that allows for the concurrent optimization of core topology and face sheet thickness of a sandwich beam under compliance constraints. The problem is solved using a novel mixed-linear extension of the Topology Optimization of Binary Structure (TOBS) topology optimization method aiming to minimize the total mass of the beam. The method has been demonstrated on a clamped beam example and the results have been compared to results from topology optimization of the core with a range of a priori fixed face sheet thicknesses. It is shown that the new method, starting from a fully populated core, finds a minimum mass that is lower than but in the neighbourhood of the best results from the topology optimization with fixed face sheet thicknesses. By varying the compliance constraint it is shown that the core topology approaches an ideal corrugated geometry as the compliance constraint is relaxed. The trends observed in the results are compared to analytical models for an idealized core.