Structural Optimization and Parallel Computation

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The proposed research will exploit parallelism in unconstrained structural optimization problems involving Finite Element Analysis (FEA). Typical engineering problems involve large finite element models and optimization algorithms take several hundred iterations. Parallel finite element analysis and optimization cannot be decoupled because calculation of gradients is closely tied with the function evaluation (FEA), requiring proper distribution of data such as global stiffness matrix and displacement solution across processors. Since the total computational cost is dominated by the cost of function evaluation, methods that result in fewer function evaluations at the expense of more linear algebraic operations per iteration might be preferred. This might require the calculation of second derivatives in order to obtain a better quadratic model. The parallelization of linear elastic finite element analysis and parallel calculation of first and/or second derivatives will be considered. In the area of biomechanics, researchers are using optimization methods to predict the distribution of material properties in the human femur due to the presence of artificial implants. Several theoretical models have been proposed. A typical model would formulate bone remodeling as an optimization problem where the objective function is strain energy and the independent variables are the material properties in each finite element. Parallel structural optimization will be used to solve some problems in this field.