In this paper a method for topology optimization of nonlinear elastic structures is suggested. The method is developed by starting from a total Lagrangian formulation of the system. The internal force is defined by coupling the second Piola-Kirchhoff stress to the Green-Lagrange strain via the Kirchhoff-St. Venant law. The state of equilibrium is obtained by first deriving the consistency stiffness matrix and then using Newton’s method to solve the non-linear equations. The design parametrization of the internal force is obtained by adopting the SIMP approach. The minimization of compliance for a limited value of volume is considered. The optimization problem is solved by SLP. This is done by using a nested approach where the equilibrium equation is linearized and the sensitivity of the cost function is calculated by the adjoint method. In order to avoid mesh-dependency the sensitivities are filtered by Sigmund’s filter. The final LP-problem is solved by an interior point method that is available in Matlab. The implementation is done for a general design domain in 2D by using fully integrated isoparametric elements. The implementation seems to be very efficient and robust.
- Design Engineering Division and Computers in Engineering Division
Topology Optimization of Non-Linear Elastic Structures by Using SLP
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Stro¨mberg, N. "Topology Optimization of Non-Linear Elastic Structures by Using SLP." Proceedings of the ASME 2009 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. Volume 5: 35th Design Automation Conference, Parts A and B. San Diego, California, USA. August 30–September 2, 2009. pp. 1261-1265. ASME. https://doi.org/10.1115/DETC2009-86292
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