Presentation of the FEM analysis methodology using MathCAD software

Author:

Králik Juraj1,Bočkaj Jozef1,Králik Jr. Juraj1

Affiliation:

1. Slovak University of Technology in Bratislava, Faculty of Civil Engineering and Faculty of Architecture and Design Vazovova 5, Bratislava 812 43 Slovakia

Abstract

This paper presents the authors' experience with teaching the finite element method (FEM) at a university using the MathCAD software. With the development of computational tools in the second half of the 20th century, there was also the development of computational methods aimed at algorithmizing engineering tasks based on FEM. This method is very effective for determining the forces and deformations of truss and frame structures under the influence of the external environment. Many processes in the automatic design system take place as if in a "black box", and the process of verifying the achieved results becomes the most important stage in the design activity. Without knowing the theoretical foundations of FEM, physical and mathematical modelling, verification procedures and methods, the structure design cannot be safe and reliable. In this paper, we present one of the possibilities, how a student can familiarize himself with the theoretical foundations of FEM and calculation procedures using the MathCAD software. MathCAD can be used as a vehicle to create, organize, and assemble all the pieces of the engineering calculations. MathCAD is open software for using input data from other programs.

Publisher

North Atlantic University Union (NAUN)

Subject

General Medicine

Reference12 articles.

1. R. Courant, Variational methods for the solution of problems of equilibrium and vibrations, Bulletin of the American Mathematical Society. Vol 49, pp. 1–23. 1943.

2. O.C. Zienkiewicz, R.L. Taylor, “The Finite Element Method. Vol. 1 The Basis, Vol .2 Solid Mechanics”, First ed. by McGraw-Hill 1967, Fifth Ed. by Butterworth-Heinemann 2000.

3. E. Madenci, I. Guven, “The Finite Element Method and Applications in Engineering Using ANSYS”, Ed. Springer, pp. 653, 2015.

4. Z. Bittnar, J. Šejnoha, “Numerical Methods in Structural Mechanics”, ASCE, pp. 470, 1996.

5. J. Králik, “Reliability Analysis of Structures Using Stochastic Finite Element Method”, Monograph. Published by STU Bratislava, pp. 143, 2009.

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