Publication

Isogeometric Analysis for the Elastic Wave Equation

2013
Student Projects

Abstract

In everyday life of an engineer, CAD (Computer Aided Design) and FE (Finite Element) programs play an important role. The two different structures, CAD and FE programs, use different mathematical functions. In CAD programs, so called NURBS find their applications while the standard functions used in FE programs are Lagrange polynomials. This differences in the structure of the two programs result in a significant effort of translation. The concept of Isogeometric Analysis tries to extend the FE method by using NURBS as basis for the analysis. In this report we give first an introduction to NURBS. We will see that, compared to a standard FE analysis, we have a richer repertory for refining a given NURBS basis. Then we will use NURBS as basis for analysis to solve numerically two problems of linear elasticity; an equilibrium problem and a simulation of an earthquake.

Official source

https://infoscience.epfl.ch/entities/publication/faf68530-fe22-4a04-8485-8cad784e1db2

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2013
Student Projects

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/faf68530-fe22-4a04-8485-8cad784e1db2

About this result

Related concepts (32)

Computer-aided design

Computer-Aided Design (CAD) is the use of computers (or ) to aid in the creation, modification, analysis, or optimization of a design. This software is used to increase the productivity of the designer, improve the quality of design, improve communications through documentation, and to create a database for manufacturing. Designs made through CAD software are helpful in protecting products and inventions when used in patent applications. CAD output is often in the form of electronic files for print, machining, or other manufacturing operations.

Finite element method

The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems).

AutoCAD

AutoCAD is a 2D and 3D computer-aided design (CAD) software application for desktop, web, and mobile developed by Autodesk. It was first released in December 1982 for the CP/M and IBM PC platforms as a desktop app running on microcomputers with internal graphics controllers. Initially a DOS application, subsequent versions were later released for other platforms including Classic Mac OS (1992), Microsoft Windows (1992), web browsers (2010), iOS (2010), macOS (2010), and Android (2011).

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Isogeometric Analysis for the Elastic Wave Equation

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