Integrated structural analysis and design using three-dimensional finite elements
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Barthelemy, B.↗
Engineering topics
Barthelemy, B.
Publications and source records attributed to Barthelemy, B..
On the accuracy of shape sensitivity
The calculation of sensitivity of the response of a structure modeled by finite elements to shape variation is known to be subject to numerical difficulties. The accuracy of a given method is typically measured against the yard stick of finite-difference sensitivity calculation. The present paper demonstrates with a simple example that this approach may be flawed because of discretization errors associated with the finite element mesh. Seven methods for calculating sensitivity derivatives are compared for a two-material beam problem with a moving interface. It is found that as the mesh is refined, displacement sensitivity derivatives converge more slowly than the displacements. Six of the methods agree fairly well, but the adjoint variational surface method provides substantially different results. However, the difference is found to reflect convergence from another direction to the same answer rather than reduced accuracy. Additionally, it is observed that small derivatives are particularly prone to accuracy problems.
Haftka, R. T.↗
Integrated structural analysis and design using 3-D finite elements
The optimum design of the shape of a hole in a plate in tension is obtained with a design algorithm based on partially converged analysis. The plate is modeled by three-dimensional finite elements, and an EBE PCG iterative solution algorithm is used for solving the equations of equilibrium. Several parametrizations of the optimum shape are considered, and it is found that a sine series can describe the optimum shape with only three design variables. The optimum shape compares well with an experimental optimum obtained by Durelli.
Barthelemy, B.↗