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Lund University Lund University Publications2000-01-01T00:00+00:001dailyTopology optimization of finite strain viscoplastic systems under transient loads
https://lup.lub.lu.se/search/publication/9334528a-7b94-4ac1-a723-7054d6a565ff
Ivarsson, NiklasWallin, MathiasTortorelli, Daniel2018-03-25A transient finite strain viscoplastic model is implemented in a gradient-based topology optimization framework to design impact mitigating structures. The model's kinematics relies on the multiplicative split of the deformation gradient, and the constitutive response is based on isotropic hardening viscoplasticity. To solve the mechanical balance laws, the implicit Newmark-beta method is used together with a total Lagrangian finite element formulation. The optimization problem is regularized using a partial differential equation filter and solved using the method of moving asymptotes. Sensitivities required to solve the optimization problem are derived using the adjoint method. To demonstrate the capability of the algorithm, several protective systems are designed, in which the absorbed viscoplastic energy is maximized. The numerical examples demonstrate that transient finite strain viscoplastic effects can successfully be combined with topology optimization.http://lup.lub.lu.se/record/9334528a-7b94-4ac1-a723-7054d6a565ffhttp://dx.doi.org/10.1002/nme.5789scopus:85044210967engInternational Journal for Numerical Methods in Engineering; 114(13), pp 1351-1367 (2018)ISSN: 0029-5981BeräkningsmatematikCrashworthinessDiscrete adjoint sensitivity analysisFinite strainRate-dependent plasticityTopology optimizationTopology optimization of finite strain viscoplastic systems under transient loadscontributiontojournal/articleinfo:eu-repo/semantics/articletextStiffness optimization of non-linear elastic structures
https://lup.lub.lu.se/search/publication/5a244785-6287-4272-81af-c8683da53e0e
Wallin, MathiasIvarsson, NiklasTortorelli, Daniel2018-03-01This paper revisits stiffness optimization of non-linear elastic structures. Due to the non-linearity, several possible stiffness measures can be identified and in this work conventional compliance, i.e. secant stiffness designs are compared to tangent stiffness designs. The optimization problem is solved by the method of moving asymptotes and the sensitivities are calculated using the adjoint method. For the tangent cost function it is shown that although the objective involves the third derivative of the strain energy an efficient formulation for calculating the sensitivity can be obtained. Loss of convergence due to large deformations in void regions is addressed by using a fictitious strain energy such that small strain linear elasticity is approached in the void regions. A well posed topology optimization problem is formulated by using restriction which is achieved via a Helmholtz type filter. The numerical examples provided show that for low load levels, the designs obtained from the different stiffness measures coincide whereas for large deformations significant differences are observed.http://lup.lub.lu.se/record/5a244785-6287-4272-81af-c8683da53e0ehttp://dx.doi.org/10.1016/j.cma.2017.11.004scopus:85034860957engComputer Methods in Applied Mechanics and Engineering; 330, pp 292-307 (2018)ISSN: 0045-7825Teknisk mekanikFinite strainsNon-linear elasticityStiffness optimizationTopology optimizationStiffness optimization of non-linear elastic structurescontributiontojournal/articleinfo:eu-repo/semantics/articletextTopology optimization based on finite strain plasticity
https://lup.lub.lu.se/search/publication/d90f1aa5-cc72-4498-bb0d-ff2146b75ed4
Wallin, MathiasJönsson, ViktorWingren, Eric2016-10In this paper infinitesimal elasto-plastic based topology optimization is extended to finite strains. The employed model is based on rate-independent isotropic hardening plasticity and to separate the elastic deformation from the plastic deformation, use is made of the multiplicative split of the deformation gradient. The mechanical balance laws are solved using an implicit total Lagrangian formulation. The optimization problem is solved using the method of moving asymptotes and the sensitivity required to form convex separable approximations is derived using a path-dependent adjoint strategy. The optimization problem is regularized using a PDE-type filter. A simple boundary value problem where the plastic work is maximized is used to demonstrate the capability of the presented model. The numerical examples reveal that finite strain plasticity successfully can be combined with topology optimization.http://lup.lub.lu.se/record/d90f1aa5-cc72-4498-bb0d-ff2146b75ed4http://dx.doi.org/10.1007/s00158-016-1435-0scopus:84964319007wos:000386356700005engStructural and Multidisciplinary Optimization; 54(4), pp 783-793 (2016)ISSN: 1615-147XAnnan maskinteknikFinite strain plasticityTopology optimizationTransient adjoint sensitivityTopology optimization based on finite strain plasticitycontributiontojournal/articleinfo:eu-repo/semantics/articletext