hp Finite Element Methods in Failure Prediction and Material Science

University Of Maryland Baltimore County, Baltimore MD

Investigators

Abstract

ABSTRACT OF PROJECT The goal of this project is to formulate, analyze and numerically test new computational algorithms geared towards solving problems of deformation and failure in structures and materials. We use the p/hp finite element methods, where the degree p of polynomials used can be increased to achieve accuracy. The first topic is the investigation of a linearized algorithm for the buckling of three-dimensional objects, recently implemented in the commercial hp code STRESS CHECK. Spurious predictions are unavoidable due to the non-compactness of an underlying eigenvalue problem. We develop a mathematical theory which analyzes the algorithm, helps in ensuring the reliability of the computations, and leads to useful extensions. The second topic is the development of a p finite element method for woven composite materials. An algorithm will be developed whereby each periodic cell is identified with a specialized p-type element, which can incorporate the various geometric and material properties. The periodicity is exploited since no mesh sub-division is used, but accuracy achieved by increasing the degree in the local elements. It is well known that when a thin vertical beam is loaded too much, it will eventually buckle. This project mathematically develops a new engineering method for predicting such maximum buckling loads for complicated three-dimensional structures. The goal is to ensure that the results predicted by the engineering method (already in use in the commercial software STRESS CHECK, which has been used e.g. to study the buckling of space shuttle panels) are reliable. The second part of this project develops a new method to computationally study woven composite materials. These materials, which are composed of fibers that are woven together and imbedded in a surrounding matrix are often both very strong and lightweight, and have several useful industrial applications (e.g. aeronautical components). Due to their complicated structure, their analysis by conventional methods can be quite cumbersome and expensive. Our new method overcomes several difficulties by exploiting the repeating nature of the material, and will lead to useful materials science applications, such as the design of new composites with specific properties.