A combined MAPLE-based system of numerical and symbolic methods in the problems of nonlinear anti-plane deformation

Abstract

MAPLE is a symbolic computation package widely used in theoretical studies. The package also contains a numerical component expanding the scope of its application. In the present paper we propose a problem-oriented automated calculation system, which is a combination of numerical methods and systems of analytical calculations (SAV) in the MAPLE environment. This solution automation system is not an alternative for well-known numerical packages, such as ANSYS, ABAQUS, etc. It just extends the universal package MAPLE, simplifies and adapts it to the problems of mechanics. Finite anti-plane deformation has been chosen for modeling because it is the simplest type of finite deformation that occurs in long rubber-metal shock absorbers. The proposed automated calculation system includes powerful symbolic integration methods, functional minimization methods, and MAPLE visualization techniques. We describe here a conceptual approach to construction of our numerical and symbolic system, MAPLE capabilities, selection and justification of the variational principle, and the contents of a subprogram library. The method is verified using a known exact solution. The calculation of shock absorber (considered as an example) does not mean that the system is designed for this purpose only. With MAPLE, one can automate the approximate solution of static problems of anti-plane finite deformation under mixed boundary conditions and arbitrary neoquassin potential for areas of complex configuration. The same calculation systems can be created for planar and axisymmetric deformations. Taken together, these blocks can give users a workplace environment in MAPLE.