Mark E. Botkin

Usage of meshfree methods in reliability analysis

This paper describes the use of meshfree methods for response and design sensitivity calculations within structural reliability analysis when geometric shape is a random variable. Brief descriptions of meshfree methods and advanced probabilistic methods are provided. An existing interface between the probabilistic analysis and traditional finite element method is modified to allow the use of meshfree methods for response and design sensitivity calculations within the probabilistic analysis routine. Three examples that treat design shape and thickness as random variables are presented to assess the accuracy and use of meshfree methods for reliability analysis.

Design Sensitivity Analysis of Nonlinear Shell Structure With Frictionless Contact

A continuum-based shape and configuration design sensitivity analysis method for a finite deformation elastoplastic shell structure with frictionless contact has been developed. Shell elastoplasticity is treated based on the projection method that performs the return mapping on the subspace defined by the zero-normal stress condition. An incrementally objective integration scheme is used in the context of finite deformation shell analysis, wherein stress objectivity is preserved for finite rotation increments. The penalty regularization method is used to approximate the contact variational inequality. The material derivative concept is used to develop continuum based design sensitivity. The design sensitivity equation is solved without iteration at each converged load step. Numerical implementation of the proposed shape and configuration design sensitivity analysis is carried out using the meshfree method. The accuracy and efficiency of the proposed method is illustrated using numerical examples.© 2003 ASME

Continuum-Based Design Sensitivity Analysis and Optimization of Springback in Stamping Process

The springback is a significant manufacturing defect in the stamping process. A serious impediment to the use of lighter-weight, higher-strength materials in manufacturing is the relative lack of understanding about how these materials respond to the complex forming process. The springback problem can be reduced by using appropriate designs of die, punch, and blank holder shape together with friction and blank holding force. That is, an optimum stamping process can be determined using a gradient-based optimization to minimize the springback. However, for an effective optimization of the stamping process, development of an efficient analytical design sensitivity analysis method is crucial. In this paper, a continuum-based shape and configuration design sensitivity analysis (DSA) method for the stamping process has been developed. The material derivative concept is used to develop the continuum-based design sensitivity. The design sensitivity equation is solved without iteration at each converged load step in the finite deformation elastoplastic nonlinear analysis with frictional contact, which makes the design sensitivity calculation very efficient. The accuracy and efficiency of the proposed method is illustrated by minimizing springback in an S-rail part, which is often used as an industrial benchmark to verify the numerical procedures employed for stamping processes.Copyright

SHAPE OPTIMIZATION OF TWO-DIMENSIONAL AUTOMOTIVE COMPONENTS USING A MESHFREE METHOD

The Reproducing Kernel Particle Method (RKPM) is one of several so-called meshfree methods of structural analysis and has been applied in this paper to the gradient-based shape optimization of two-dimensional automotive components. As indicated by the term meshfree, no mesh is required, but rather a field of points, or particles, are distributed within the domain of the problem. Three standard linear examples are chosen to allow a comprehensive comparison between the optimization with the RKPM and the state-of-art optimization tool in Unigraphics Version 18 (UG V18). The results show that the optimization analysis with the RKPM is able to accommodate very large shape changes required in the optimization process without doing particle re-adaptation, and provides accurate solutions of the objective and constraint functions and their gradients, therefore facilitates a fast convergence of the gradient-based optimization algorithm.