This paper proposes a method for performing both multi-material topology optimization and multi-joint topology optimization. The algorithm can determine the optimum placement and selection of ...material while also optimizing the choice and placement of joint material between components. This method can simultaneously minimize the compliance of the structure as well as the total joint cost while subjected to a mass fraction constraint. A decomposition approach is used to break up the coupling between optimum structural design and optimum joint design. Multi-material and multi-joint topology optimization are then solved sequentially, controlled by an outer loop. By decomposing the problem, gradient-based optimization algorithms can be utilized, enabling the algorithm to solve large computational models efficiently. The proposed process is applied to three 3D standard TO problems. Through these example problems, the need for an iterative process is demonstrated. Improvements to joint manufacturability using the tooling and stress constraints are discussed. Finally, a review of computational cost is performed.
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EMUNI, FIS, FZAB, GEOZS, GIS, IJS, IMTLJ, KILJ, KISLJ, MFDPS, NLZOH, NUK, OBVAL, OILJ, PNG, SAZU, SBCE, SBJE, SBMB, SBNM, UKNU, UL, UM, UPUK, VKSCE, ZAGLJ
In this paper, a level‐set‐based method is presented to deal with the multi‐material topology optimization of compliant mechanisms with stress constraints. A novel stress‐based multi‐material ...topology optimization model of compliant mechanisms is proposed. In this model, the multi‐material level set topology description model and the separable stress interpolation scheme are adopted. The weighted sum method is used to deal with the multi‐objective optimization of the output displacement and compliance of compliant mechanisms. The penalty of stresses is also considered in the objective function to control the local stress level in different materials. To solve the optimization problem, the parametric level set method is employed, and the sensitivity analysis is conducted. Application of the method is demonstrated by 2 numerical examples. Results show that the multi‐material structures without undesirable de facto hinges can be obtained. The output displacement and compliance of the compliant mechanisms are optimized, and stress constraints in different materials are simultaneously satisfied.
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A three-dimensional (3D) topology optimization approach based on extruded geometric components (EGCs) is proposed. Each EGC is constructed by extruding a convex/non-convex polygon along the axis of ...the EGC and rounding the ends of the EGC. Using an adaptive mapping technique which allows mapping each ECG onto a support domain, the EGCs are mapped onto an analytical grid to obtain an effective density field for material interpolation. Moreover, 2D-plane calculations can be utilized to replace 3D-space calculations to enhance computing efficiency. The positions and the cross-sectional areas of the ECGs are simultaneously optimized through the determination of an optimum set of geometry parameters. Some structural benchmark problems were investigated to verify the applicability of the proposed approach. Compared with the solid isotropic material penalization (SIMP) approach, the underlying approach does not require any filtering or projection techniques. Hence, it can produce a stiffer optimum design with an explicit boundary description whilst the number of design variables dramatically reduces.
•Extruded geometric component (EGC) is modeled with geometry parameters.•EGC-based 3D topology optimization is proposed.•Adaptive mapping technique projects a geometric component onto a fit subdomain.•2D-plane computation is utilized to replace 3D-space computation.•Minimum length scale obtained by setting a lower bound for thickness parameters.
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This paper proposes a new multiscale topology optimization method for the design of porous composites composed of the multi-domain material microstructures considering three design elements: the ...topology of the macrostructure, the topologies of multiple material microstructures and their overall distribution in the macrostructure. The multiscale design involves two optimization stages: the free material distribution optimization and the concurrent topology optimization. Firstly, the variable thickness sheet (VTS) method with the regularization mechanism is used to generate multiple element density distributions in the macro design domain. Hence, different groups of elements with the identical densities can be uniformly arranged in their corresponding domains, and each domain in the space will be periodically configured by a unique representative microstructure. Secondly, with the discrete material distributions achieved in the macro domain, the topology of the macrostructure and topologies of multiple representative microstructures are concurrently optimized by a parametric level set method combined with the numerical homogenization method. Finally. Several 2D and 3D numerical examples are provided to demonstrate the effectiveness of the proposed multiscale topology optimization method.
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Advances in additive manufacturing (AM) have drawn considerable interest due to its ability to produce geometrically complex structure, such as lattice materials. In this work, a novel methodology is ...proposed to design graded lattice structure through topology optimization under stress constraint, in order to generate lightweight lattice structure design with predictable yield performance. Instead of using the power law of material interpolation in the SIMP method, asymptotic homogenization method is employed to compute the effective elastic properties of lattice material in terms of design variable, i.e. relative density. For yield strength, a multiscale failure model is proposed to capture yield strength of microstructure with macroscopic stress. At macroscale, a modified Hill’s yield criterion is employed to describe anisotropic yield strength of lattice material. The material constants in Hill’s model are assumed to be a function of relative density, and thus a model is built up to formulate yield strength of lattice structure with macroscopic stress. The experimental verification on the printed samples demonstrates that both the homogenized elastic model and yield model can accurately describe the elasticity and plasticity of the lattice structure. Based on the proposed material interpolation for lattice structure, a lattice structure topology optimization framework is proposed for minimizing total weight of the structure under stress constraint. The sensitivity analysis is performed for the implementation of the optimization algorithm. Two three-dimensionally numerical examples are performed to demonstrate the effectiveness of the proposed optimization method, as well as accuracy of the proposed homogenization technique for graded lattice structure design. Experiment is conducted to systematically examine yielding of the optimally graded lattice structure design and compare its performance with a uniform structure. It is found that the proposed optimization framework is valid for the design examples examined and can significantly enhance mechanical performance of the structure (i.e. yield loading, stiffness, energy absorption, etc.)
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Graded lattice sandwich structures (GLSSs) enable superior structural performances due to the continuously-varying configurations and properties of lattices in space. This paper proposes a design ...method for GLSSs by multiscale topology optimization. In this method, the geometrical configuration of a prototype lattice cell (PLC) is described by an explicit topology description function (TDF). Based on some sample lattice cells, a Kriging metamodel is constructed to predict the effective property of each lattice cell. Based on the Kriging metamodel, the thickness optimization of two solid face-sheets and the distribution optimization of lattice cells in core layer are respectively implemented. Driven by their equivalent densities, the configurations of lattice cells with similar topological features are generated by interpolating the shape of the PLC. Then, the graded lattice cells (GLCs) are generated. Using the proposed method, the computational burden involved in design of GLSSs can be reduced significantly. What is more, the manufacturability of GLSSs can be guaranteed by constructing a proper PLC with the help of TDF. Numerical examples in terms of compliance and natural frequency optimization of GLSSs are provided to verify the advantages of the proposed method. Also, bending tests are performed on the GLSSs fabricated by additive manufacturing (AM). The results reveal that GLSSs are stiffer and have larger natural frequencies than the uniform lattice sandwich structures.
•A design method for graded lattice sandwich structures by multiscale topology optimization.•Geometrical configurations of graded lattices are obtained based on explicit description function.•Numerical examples under different design situations are presented.•Experimental tests are conducted to show superior performance of optimized sandwich structures.
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18.
Multimaterial multijoint topology optimization Woischwill, Christopher; Kim, Il Yong
International journal for numerical methods in engineering,
28 September 2018, Volume:
115, Issue:
13
Journal Article
Peer reviewed
Summary
In this paper, a methodology that solves multimaterial topology optimization problems while also optimizing the quantity and type of joints between dissimilar materials is proposed. ...Multimaterial topology optimization has become a popular design optimization technique since the enhanced design freedom typically leads to superior solutions; however, the conventional assumption that all elements are perfectly fused together as a single piece limits the usefulness of the approach since the mutual dependency between optimal multimaterial geometry and optimal joint design is not properly accounted for. The proposed methodology uses an effective decomposition approach to both determine the optimal topology of a structure using multiple materials and the optimal joint design using multiple joint types. By decomposing the problem into two smaller subproblems, gradient‐based optimization techniques can be used and large models that cannot be solved with nongradient approaches can be solved. Moreover, since the joining interfaces are interpreted directly from multimaterial topology optimization results, the shape of the joining interfaces and the quantity of joints connecting dissimilar materials do not need to be defined a priori. Three numerical examples, which demonstrate how the methodology optimizes the geometry of a multimaterial structure for both compliance and cost of joining, are presented.
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This paper investigates reliability-based topology optimization (RBTO) and proposes a novel quantile-based topology optimization (QBTO) method. With this method, the traditional RBTO model is ...transformed into an equivalent quantile-based formulation, which can well avoid the issues existing in RBTO with Monte Carlo simulation (MCS), i.e., stagnation of optimizer due to near zero sensitivities of probabilistic constraint with regard to element densities, huge computational cost on calculating sensitivities, and the discontinuity of failure indicator function. Specially, in QBTO, the sensitivities only require to be calculated at the sample corresponding to the quantile instead of all MCS samples, which can drastically reduce the computational effort. Furthermore, a sequential update strategy of Kriging metamodel is developed to efficiently calculate the quantile by evaluating the true constraint at fewer samples, rather than all MCS samples. The high accuracy and efficiency of QBTO are validated by truss, beam and bridge problems.
•A quantile-based topology optimization (QBTO) method is proposed.•QBTO can well avoid the issues existing in reliability-based topology optimization with Monte Carlo simulation.•A sequential update strategy of Kriging metamodel is developed to efficiently calculate the quantile.•The high accuracy and efficiency of QBTO are validated by truss, beam and bridge problems.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
With the diversification of engineering structure performance requirements and the continuous development of structural design refinement, it puts forward higher requirements for lightweight design ...of structures in terms of concurrent design and reliability design. It is necessary to develop advanced design technology. This paper focuses on the influence of multi-source hybrid uncertainties and defect damage in the design process and proposes a concurrent reliability-based topology optimization design method. Based on the collocation method, the propagation analysis of hybrid uncertainties is realized. A performance reduction method considering defect damage is proposed. Furthermore, the parameter iteration strategy of the optimization criterion method is improved. Based on the sensitivity analysis of a series of parameters, the gradient optimization algorithm is used to solve the optimization model. Finally, three numerical examples are given to illustrate the effectiveness and necessity of the proposed method.
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