A major bottleneck in integration of finite element or finite difference-based Computer Aided Engineering (CAE) tools with industrial Computer Aided Design (CAD) and Computer Aided Manufacturing (CAM) tools is the generation of well-shaped meshes that are consistent with complex CAD models and which provide computational accuracy and efficiency of numerical solutions, particularly for nonlinear simulation and design of manufacturing processes. A meshless-based numerical method is planned to provide seamless integration through CAD geometry, simulation, and shape design optimization. The method can be directly linked to CAD geometries since the shape/interpolation functions in the meshless method are formulated independent of the background integration zone. The meshless method will provide a higher rate of convergence and alleviate many numerical difficulties with respect to mesh distortion and moving continuities encountered in conventional finite element methods. A meshless formulation for linear and nonlinear problems involving elastic and inelastic materials and contact conditions will be developed. Efficient computable error estimates will be derived for the meshless formulation. Nodal integration methods will be formulated to enhance efficiency, and adaptive meshless methods will be developed for controlling accuracy and efficiency in large deformation problems. Development and implementation of the meshless methods will be accomplished using scalable and portable high-performance algorithms optimized for use in parallel processor computer environments. New, fast graph partitioning techniques and hierarchical methods for subdividing the domain will be used to gain maximum benefits in computational speed and efficiency from parallel processor computers. A meshless shape design sensitivity analysis method that exploits the CAD-linked geometries will be developed for rapid, robust design.
The objective of the planned research is to achieve technology solutions that promote seamless and substantive interaction between diverse design and engineering analysis disciplines throughout the production process, from concept development to manufacturing. The technology developed under this effort will remove major impediments to comprehensive collaboration between product designers and engineers by maintaining a high degree of coherence between CAD, CAE and CAM modeling and simulation, as well as by significantly enhancing the speed and relevance of design information which designers and engineers exchange during all stages of the product development process. Achieving the meshless-based integration of CAD, engineering simulation, and design will have substantial positive impact with respect to cost reduction, mature design development, and reduced time-to-market by enabling more extensive use of accurate and reliable simulation-based engineering and design methods in lieu of costly and time-consuming prototype design, test, and evaluation. The application of the meshless technology is also designed to take maximum advantage of high-performance computer capabilities that are in widespread use in industry.
The research program to be carried out under this effort will expedite validation of meshless methods and technology transfer to industry. A partnership with Ford Motor Company has been established under which Ford's Research Laboratory will commit to an open exchange of data and expertise, as well as personnel resources for testing and validating meshless methods and their implementation on high performance computer platforms. Planned internship programs, graduate and undergraduate student participation, academic seminars, creation of new academic courses, reports and publications, and an international workshop will provide a range of options for practical and effective dissemination of the results and technical accomplishments of this effort.
Funding for this activity will be provided by the Division of Mathematical Sciences, the MPS Office of Multidisciplinary Activities, and by DARPA.
