A simple evolutionary topology optimization procedure for compliant mechanism design

Ansola, Rubén; Veguería, Estrella; Canales, J.; Tárrago, J. A.

doi:10.1016/j.finel.2007.09.002

Cited by 79 publications

(39 citation statements)

References 23 publications

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“…A direct triangulation of O or its boundary would probably work with all regularizations, but would require remeshing during the optimization and induce technical difficulties with topological changes. The so-called evolutionary structural optimization (ESO) is based on discretizing the computational domain by finite elements and successively removing those elements which contribute least to the structural stiffness (or another chosen objective, see for example [10]). This corresponds to a regularization via discretization and thereby introduces a mesh dependence.…”

Section: Related Workmentioning

confidence: 99%

A phase-field model for compliance shape optimization in nonlinear elasticity

2010

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Abstract. Shape optimization of mechanical devices is investigated in the context of large, geometrically strongly nonlinear deformations and nonlinear hyperelastic constitutive laws. A weighted sum of the structure compliance, its weight, and its surface area are minimized. The resulting nonlinear elastic optimization problem differs significantly from classical shape optimization in linearized elasticity. Indeed, there exist different definitions for the compliance: the change in potential energy of the surface load, the stored elastic deformation energy, and the dissipation associated with the deformation. Furthermore, elastically optimal deformations are no longer unique so that one has to choose the minimizing elastic deformation for which the cost functional should be minimized, and this complicates the mathematical analysis. Additionally, along with the non-uniqueness, buckling instabilities can appear, and the compliance functional may jump as the global equilibrium deformation switches between different bluckling modes. This is associated with a possible non-existence of optimal shapes in a worst-case scenario. In this paper the sharp-interface description of shapes is relaxed via an Allen-Cahn or Modica-Mortola type phase-field model, and soft material instead of void is considered outside the actual elastic object. An existence result for optimal shapes in the phase field as well as in the sharp-interface model is established, and the model behavior for decreasing phase-field interface width is investigated in terms of Γ-convergence. Computational results are based on a nested optimization with a trust-region method as the inner minimization for the equilibrium deformation and a quasi-Newton method as the outer minimization of the actual objective functional. Furthermore, a multi-scale relaxation approach with respect to the spatial resolution and the phase-field parameter is applied. Various computational studies underline the theoretical observations. Mathematics Subject Classification. 49Q10, 74P05, 49J20.

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Section: Related Workmentioning

confidence: 99%

A phase-field model for compliance shape optimization in nonlinear elasticity

2010

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“…Finite element method is often used for structural analysis and some specific mechanism called compliant mechanism. A compliant mechanism is a mechanism that gains some or all of its mobility from the flexibility of its components [18].Thus, compliant mechanism can easily be analyzed by finite element, but not for general mechanisms.…”

Section: Review Of Kinematics Analysismentioning

confidence: 99%

Topology and Dimensional Synthesis of Linkage Mechanism Based on the Constrained Superposition Method

Chen

Chang

Gea

2008

Volume 1: 34th Design Automation Conference, Parts a and B

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“…These were, among others: Genetic Algorithms [11], Level Set Methods [12] and the Evolutionary Structural Optimization (ESO) method [13]. The first two methods were also extended to cover further applications such as path generation mechanisms [14][15], design of multiphysics actuators [8] [16] and non linear analysis [17][18] [19].…”

Section: Introductionmentioning

confidence: 99%

“…The method proposed by Ansola et al [13] used the additive version of the method, AESO [20]. The method worked by starting from an empty design domain (most compliant mechanism) with material gradually added until the target volume was achieved.…”

Section: Introductionmentioning

confidence: 99%