Stiffness optimization of geometrically nonlinear structures and the level set based solution

Xia, Qi; Shi, Tielin

doi:10.1051/smdo/2016002

Cited by 10 publications

(3 citation statements)

References 37 publications

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“…This equivalence does not extend to the non-linear regime. In fact, as reported by [30,32], the end-compliance might not be the best measure to characterise stiffness in this regime, and instead, they advocate for the minimisation of the complementary work. However, the scope of this paper is not on the suitability of the objective function in order to characterise the stiffness of the structure, but rather, on presenting a new methodology that can address the numerical difficulties in TO by means of the SIMP method, which manifest regardless of the choice of objective function.…”

Section: Introductionmentioning

confidence: 95%

“…Several authors have ventured in the field of structural TO at large displacements/strains by using either polyconvex constitutive models or the Saint Venant-Kirchhoff model 4 [12,15,[24][25][26][27][28][29][30][31][32], where some strategies have been put forward to overcome some of the instabilities associated with intermediate density regions. For instance, the additive hyperelasticity technique presented in [33]; the combination of a polyconvex strain energy density in conjunction with an ad-hoc relaxation introduced in [27] to stabilise those excessively distorted elements of an underlying Finite Element mesh, or an original interpolation scheme for the strain energy density as proposed in [15].…”

Section: Introductionmentioning

confidence: 99%

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A stabilisation approach for topology optimisation of hyperelastic structures with the SIMP method

Ortigosa

Ruiz

Gil

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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This paper presents a novel computational approach for SIMP-based Topology Optimisation (TO) of hyperelastic materials at large strains. During the TO process for structures subjected to very large deformations, and especially in the presence of intermediate density regions, the standard Newtonsolver (or its arc length variant) have been reported not to converge (refer to References [15,27,33]). In this paper, the new TO stabilisation technique proposed in [1] in the context of level-set TO, initially devised to alleviate numerical instabilities inherent to level-set TO, is extended for the TO by means of the SIMP method. The success of the methodology rests on the combination of two distinct key ingredients. First, the nonlinear equilibrium equations of motion for intermediate TO design stages are solved in a non-exact albeit consistent incrementally linearised fashion by splitting the design load into a number of load increments. Second, the resulting linearised tangent elasticity tensor is locally stabilised (regularised) in order to prevent its loss of positive definiteness and, thus, avoid the loss of convexity of the discrete tangent operator. This solution strategy is shown to be extremely robust in the context of density-based TO, where the constitutive law of the underlying evolving solid structure is a mixture of solid and void constituents, the latter classically defined by means of a fictitious strain energy. The robustness and applicability of this TO methodological approach are thoroughly demonstrated through an ample spectrum of challenging numerical examples, ranging from benchmark two-dimensional (plane stress) examples to larger scale three-dimensional applications. Crucially, the performance of all the final designs has been tested at a post-processing stage without adding any source of artificial stiffness. Specifically, an arc-length Newton-Raphson method has been employed in conjunction with a ratio of the material parameters for void and solid regions of 10 −12 .

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Section: Introductionmentioning

confidence: 95%

Section: Introductionmentioning

confidence: 99%

A stabilisation approach for topology optimisation of hyperelastic structures with the SIMP method

Ortigosa

Ruiz

Gil

et al. 2020

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

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“…The adjoint method performed to derive sensitivities of the objective function under nonlinear geometrically problem by the structure was optimized based on SIMP [8,9] and bi-directional evolutionary optimization (BESO) [10] methods. Xia and Shi [11] used the level set technique with Kreisselmeier-Steinhauser (KS) function to maximize stiffness for the geometrically nonlinear structure while the particle method was adopted to optimize an elastic structure with large deformation based on level set function [12]. Sequential piecewise linear programming (SPLP) was proposed for solving the geometrically nonlinear problem by including the second order of the objective function and converted into a linear problem to speed up the algorithm [13].…”

Section: Introductionmentioning

confidence: 99%

Optimization on mechanical structure for material nonlinearity based on proportional topology method

Kongwat

Hasegawa

2019

JASSE

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Topology optimization is one complex method due to a final layout obtained by an initial shape is not a consideration. This paper purposes a proportional technique to determine an optimal layout by employing the topology optimization method. The objective function is to maximize an internal energy density by stress constraint based on the bi-linear elastoplasticity material properties. Fully stress design criterion is concerned to be a factor of the proportional technique for updating the design variable. Finally, the optimal layout acquires from the proportional technique and results are faster to converge with an over-relaxation factor which applied to the fully stress design.

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A passive load alleviation aircraft wing: topology optimization for maximizing nonlinear bending–torsion coupling

Thel

Hahn

Haupt

et al. 2022

Struct Multidisc Optim

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Aircraft wings with passive load alleviation morph their shape to a configuration where the aerodynamic forces are reduced without the use of an actuator. In our research, we exploit geometric nonlinearities of the inner wing structure to maximize load alleviation. In order to find designs with the desired properties, we propose a topology optimization approach. Passive load alleviation is achieved through bending–torsion coupling. The wing twist will reduce the angle of attack, thus lowering the aerodynamic forces. Consequently, the objective function is to maximize the torsion angle. Since shape morphing should only affect loads that exceed normal maneuvering loads, a displacement constraint is enforced, preventing torsion at lower force levels. Maximizing the displacement will lead to topologies for which the finite element solver cannot find a solution. To circumvent this, we propose adding a compliance value to the objective function. This term has a weighting function, which controls how much influence the compliance value has: after a set number of iterations, the initially high level of influence will drop. We used a geometric nonlinear finite element formulation with a linear elastic material model. The addition of an energy interpolation scheme reduces mesh distortion. We successfully applied the proposed methodology to two different test cases resembling an aircraft wing box section. These test cases illustrate the methodology’s potential for designing new geometries with the desired nonlinear behavior. We discuss what design features can be deduced and how they achieve the nonlinear structural response.

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Stiffness optimization of geometrically nonlinear structures and the level set based solution

Cited by 10 publications

References 37 publications

A stabilisation approach for topology optimisation of hyperelastic structures with the SIMP method

A stabilisation approach for topology optimisation of hyperelastic structures with the SIMP method

Optimization on mechanical structure for material nonlinearity based on proportional topology method

A passive load alleviation aircraft wing: topology optimization for maximizing nonlinear bending–torsion coupling

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