A fast solver for finite deformation contact problems

We present a new solver for large-scale two-body contact problems in nonlinear elasticity. It is based on an SQP-trust-region approach. This guarantees global convergence to a first-order critical point of the energy functional. The linearized contact conditions are discretized using mortar elements. A special basis transformation known from linear contact problems allows to use a monotone multigrid solver for the inner quadratic programs. They can thus be solved with multigrid complexity. Our algorithm does not contain any regularization or penalization parameters, and can be used for all hyperelastic material models

On topology optimization and canonical duality method

Topology optimization for general materials is correctly formulated as a bi-level knapsack problem, which is considered to be NP-hard in global optimization and computer science. By using canonical duality theory (CDT) developed by the author, the linear knapsack problem can be solved analytically to obtain global optimal solution at each design iteration. Both uniqueness, existence, and NP-hardness are discussed. The novel CDT method for general topology optimization is refined and tested by both 2-D and 3-D benchmark problems. Numerical results show that without using filter and any other artificial technique, the CDT method can produce exactly 0-1 optimal density distribution with almost no checkerboard pattern. Its performance and novelty are compared with the popular SIMP and BESO approaches. Additionally, some mathematical and conceptual mistakes in literature are explicitly addressed. A brief review on the canonical duality theory for modeling multi-scale complex systems and for solving general nonconvex/discrete problems are given in Appendix. This paper demonstrates a simple truth: elegant designs come from correct model and theory. © 201

MINIMIZING THE ACOUSTIC COUPLING OF FLUID LOADED PLATES USING TOPOLOGY OPTIMIZATION

Optimization of the topology of a plate coupled with an acoustic cavity is investigated in an attempt to minimize the fluid-structure interactions at different structural frequencies. A mathematical model is developed to simulate such fluid-structure interactions based on the theory of finite elements. The model is integrated with a topology optimization approach which utilizes the Moving Asymptotes Method. The obtained results demonstrate the effectiveness of the proposed approach in simultaneously attenuating the structural vibration and the sound pressure inside the acoustic domain at several structural frequencies by proper redistribution of the plate material. Prototypes of plates with optimized topologies are manufactured at tested to validate the developed theoretical model. The performance characteristics of plates optimized for different frequency ranges are determined and compared with the theoretical predictions of the developed mathematical model. A close agreement is observed between theory and experiments. The presented topology optimization approach can be an invaluable tool in the design of a wide variety of critical structures which must operate quietly when subjected to fluid loading