Applications of symbolic and algebraic manipulation software in solving applied mechanics problems.

Abstract

As its name implies, symbolic and algebraic manipulation is an operational tool which not only can retain symbols throughout computations but also can express results in terms of symbols. This dissertation starts with a history of symbolic and algebraic manipulators and a review of the literatures. With the help of selected examples, the capabilities of symbolic and algebraic manipulators are demonstrated. Three applications to problems of applied mechanics are then presented. They are the application of automatic formulation to applied mechanics problems, application to a materially nonlinear problem (rigid-plastic ring compression) by FEM, and application to plate problems by FEM. At the end of the dissertation, the advantages and difficulties, contributions, education and perspectives of symbolic and algebraic manipulation are discussed. It is well known that there exist some fundamental difficulties in symbolic and algebraic manipulation, such as internal swelling and mathematical limitation. This dissertation proposes a remedy for these difficulties, and successfully solves the three applications mentioned above. For example, the closed form solution of stiffness matrix of four-node isoparametrical quadrilateral element for 2-D elasticity problem was not available before. Due to the work presented here, the automatic construction of it became feasible. In addition, a new advantage of the application of symbolic and algebraic manipulation found in this dissertation is believed to be crucial in improving the efficiency of program execution in the future. This will substantially shorten the response time of a system. It is very significant for certain systems, such as missile and high speed aircraft systems, in which time plays an important role.