Geometrically nonlinear design of compliant mechanisms: Topology and shape optimization with stress and curvature constraints

Stankiewicz, Gabriel; Dev, Chaitanya; Steinmann, Paul

doi:10.1016/j.cma.2022.115161

Cited by 11 publications

(10 citation statements)

References 48 publications

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“…In this work, we are dedicated to addressing the two most common and important issues involved in the MIMO compliant mechanism synthesis. One is the de facto hinge problem, which is solved by striking a good balance between structural flexibility and stiffness with the weighted objective function (8); the other is the movement coupling issue, and it is tackled through the introduction of multi-constraint conditions used to suppress both the output and input decouplings. Numerical examples show that the proposed optimization model ( 13) is effective in handling both problems.…”

Section: Discussionmentioning

confidence: 99%

“…After the introduction of input and output compliances (C Ii and C Oi ) computed by Equations ( 6) and ( 7) into the objective function ( 4), the new formulation based on the weighted sums of the flexibility and stiffness is developed as (8) in which w Ii and w Oi are the weighting factors of C Ii and C Oi , respectively. Similar to the factor ω i , both the w Ii and w Oi change with iterations adaptively as follows:…”

Section: Objective Function With the Effect Of Eliminating De Facto H...mentioning

confidence: 99%

“…The advantages of compliant mechanisms have aroused considerable and increasing interest in synthesis methods of compliant mechanisms that can be classified into two main categories: kinematic-based approaches [6,7] and structural topology optimization approaches [8,9]. The design method adopted in this work belongs to the latter category, because the topology optimization technique, which could facilitate designers to break through traditional institutions and experience, has already proven to be a powerful tool to obtain competitive and innovative mechanical and architectural structures [10][11][12].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Topology Optimization Design of Multi-Input-Multi-Output Compliant Mechanisms with Hinge-Free Characteristic and Totally Decoupled Kinematics

et al. 2023

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A new multi-constraint optimization model with the weighted objective function is proposed to design the multi-input-multi-output (MIMO) compliant mechanisms. The main feature of this work is that both the two notable problems related to the de facto hinge and the movement coupling are tackled simultaneously in the topological synthesis of MIMO compliant mechanisms. To be specific, the first problem is the severe stress concentration in the flexible hinge areas, and it is solved by the introduction of input and output compliances into the objective function, which could facilitate the optimization to strike a good balance between structural flexibility and stiffness. The second problem is the high degree of control complexity caused by the coupled outputs and inputs, and it is addressed by achieving the complete decoupling with two groups of extra constraints that are used to suppress the input coupling and the output coupling, respectively. As the most common and effective topology optimization method, the Solid Isotropic Material with Penalization (SIMP)-based density method is adopted here to obtain the optimized configurations. After the analytical sensitivity deduction related to the weighted objective function and constraints, two typical numerical examples are presented to demonstrate the validity of the proposed topology optimization framework in designing the hinge-free and completely decoupled MIMO compliant mechanisms.

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Section: Discussionmentioning

confidence: 99%

Section: Objective Function With the Effect Of Eliminating De Facto H...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Topology Optimization Design of Multi-Input-Multi-Output Compliant Mechanisms with Hinge-Free Characteristic and Totally Decoupled Kinematics

et al. 2023

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“…To profit from the advantages of different structural optimization approaches, various combined methods were proposed (Sokolowski and Zochowski, 1999;Norato et al, 2007;Eschenauer et al, 1994;Christiansen et al, 2014;Lian et al, 2017;Riehl and Steinmann, 2015;Nguyen et al, 2020;Andreasen et al, 2020;Stankiewicz et al, 2021). In our work, we adapt the sequential approach as in Dev et al (2022); Stankiewicz et al (2022), in which a standard, density-based topology optimization is used to generate an initial structure and node-based shape optimization using EDD follows up to fine tune the design. This combination proved to be a good fit due to a number of reasons.…”

Section: Introductionmentioning

confidence: 99%

“…Secondly, a coarsely discretized domain for topology optimization is chosen, as we do not require highly accurate state problem computations, since it only provides the initial configuration of the shape optimization step. Next, we incorporate a shape curvature constraint as in Stankiewicz et al (2022) to improve manufacturability and durability of the final design, which is otherwise a challenging task in topology optimization due to the lack of an explicit boundary. Finally, we exploit the advantages of both topology and shape optimization, as listed before, to provide a versatile and powerful structural optimization routine capable of designing complex geometries from a large design space, at the same time guaranteeing high accuracy of the state problem solutions and a variety of possible constraints.…”

Section: Introductionmentioning

confidence: 99%

Towards advanced piezoelectric metamaterial design via combined topology and shape optimization

Stankiewicz,

Dev,

Weichelt

et al. 2023

Preprint

Self Cite

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Metamaterials open up a spectrum of artificially engineered properties otherwise unreachable in conventional bulk materials. For electromechanical energy conversion systems, lightweight materials with high hydrostatic piezoelectric coupling coefficients and negative Poisson's ratio can be obtained. Thus, in this contribution, we explore the possibilities of piezoelectric metamaterials design by employing structural optimization. More specifically, we apply a sequential framework of topology and shape optimization to design piezoelectric metamaterials with negative Poisson's ratio for electromechanical energy conversion under uniform pressure. Topology optimization is employed to generate the initial layout, whereas shape optimization fine tunes the design and improves durability and manufacturability of the structures with the help of a curvature constraint. An embedding domain discretization (EDD) method with adaptive domain and shape refinement is utilized for an efficient and accurate computation of the state problem in the shape optimization stage. Multiple case studies are conducted to determine the importance of desired stiffness characteristics, symmetry conditions and objective formulations on the design of piezoelectric metamaterials. Results show that the obtained designs are highly dependent on the desired stiffness characteristics. Moreover, the addition of the EDD-based shape optimization step introduces significant changes to the designs, confirming the usability of the sequential framework.

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IGA-based topology optimization in the design of stress-constrained compliant mechanisms

Villalba,

Gonçalves,

Dias-de-Oliveira

et al. 2023

Struct Multidisc Optim

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Topology design of compliant mechanisms has gained wide popularity among the scientific community, and their use in the mechanical engineering field is being of upmost importance. In this paper, an isogeometric analysis (IGA) formulation is used to solve the topology optimization problem of compliant mechanisms. Stress constraints are introduced in the problem to guarantee the attainment of realistic solutions. For this purpose, an overweight constraint is considered for the design process, replacing the use of local stress constraints. The material distribution in the domain is modeled with quadratic B-splines and with a uniform relative density within each element of the mesh. These strategies to define the material layout are used to compare the IGA-based formulation with the finite element (FEM) formulation. The IGA formulation provides several advantages with respect to the classical FEM-based approaches that are shown and analyzed with an input-parameters sensitivity analysis. The sensitivity analysis and the assessment of the importance of introducing of stress constraints in the problem are developed by solving two benchmark problems. Regarding the sensitivity analysis of input parameters, the results show that the ratio between the material and the springs stiffnesses is the parameter with the largest influence on the solutions of the problem. Moreover, the advantages of the IGA formulations over FEM formulations are related with the computational time, the smoothness of the structural borders, and the non-appearance of the checkerboard patterns. With respect to the stress constraints, the results show that they have to be considered in order to avoid instability and structural integrity problems.

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Geometrically nonlinear design of compliant mechanisms: Topology and shape optimization with stress and curvature constraints

Cited by 11 publications

References 48 publications

Topology Optimization Design of Multi-Input-Multi-Output Compliant Mechanisms with Hinge-Free Characteristic and Totally Decoupled Kinematics

Topology Optimization Design of Multi-Input-Multi-Output Compliant Mechanisms with Hinge-Free Characteristic and Totally Decoupled Kinematics

Towards advanced piezoelectric metamaterial design via combined topology and shape optimization

IGA-based topology optimization in the design of stress-constrained compliant mechanisms

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