A Fortran implementation of isogeometric analysis for thin plate problems with the penalty method

Abstract

Purpose

As one of the earliest high-level programming languages, Fortran with easy accessibility and computational efficiency is widely used in the engineering field. The purpose of this paper is to present a Fortran implementation of isogeometric analysis (IGA) for thin plate problems.

Design/methodology/approach

IGA based on non-uniform rational B-splines (NURBS) offers exact geometries and is more accurate than finite element analysis (FEA). Unlike the basis functions in FEA, NURBS basis functions are non-interpolated. Hence, the penalty method is used to enforce boundary conditions.

Findings

Several thin plate examples based on the Kirchhoff-Love theory were illustrated to demonstrate the accuracy of the implementation in contrast with analytical solutions, and the efficiency was validated in comparison with another open method.

Originality/value

A Fortran implementation of NURBS-based IGA was developed to solve Kirchhoff-Love plate problems. It easily obtained high-continuity basis functions, which are necessary for Kirchhoff formulation. In comparison with theoretical solutions, the numerical examples demonstrated higher accuracy and faster convergence of the Fortran implementation. The Fortran implementation can well solve the time-consuming problem, and it was validated by the time-consumption comparison with the Matlab implementation. Due to the non-interpolation of NURBS, the penalty method was used to impose boundary conditions. A suggestion of the selection of penalty coefficients was given.

Citation

Chang, F., Wang, W., Liu, Y. and Qu, Y. (2016), "A Fortran implementation of isogeometric analysis for thin plate problems with the penalty method", Engineering Computations, Vol. 33 No. 7, pp. 2149-2164. https://doi.org/10.1108/EC-10-2015-0306