ANALYTICAL SOLUTION FOR FIXED-FIXED ANISOTROPIC BEAM SUBJECTED TO UNIFORM LOAD

• Published in: Applied mathematics and mechanics Vol. 27; no. 10; pp. 1305 - 1310
• Main Author: 丁皓江 黄德进 王惠明
• Format: Journal Article
• Language: English
• Published: Faculty of Engineering,Ningbo University,Ningbo 315211,Zhejiang Province,P.R.China%Department of Mechanics,Zhejiang University,Hangzhou 310027,P.R.China 01.10.2006; Department of Civil Engineering,Zhejiang University,Hangzhou 310027,P.R.China%Department of Civil Engineering,Zhejiang University,Hangzhou 310027,P.R.China
• Subjects: Anisotropy; Beams (structural); Boundary conditions; Finite element method; Mathematical analysis; Mathematical models; Stress functions; Stresses; 各向异性; 应力函数; 未知系数; 解析解; analytical solution; stress function; fixed-fixed beam; anisotropy
• ISSN: 0253-4827; 1573-2754
• DOI: 10.1007/s10483-006-1002-z

The analytical solutions of the stresses and displacements were obtained for fixed-fixed anisotropic beams subjected to uniform load. A stress function involving unknown coefficients was constructed, and the general expressions of stress and displacement were obtained by means of Airy stress function method. Two types of the description for the fixed end boundary condition were considered. The introduced unknown coefficients in stress function were determined by using the boundary conditions. The analytical solutions for stresses and displacements were finally obtained. Numerical tests show that the analytical solutions agree with the FEM results. The analytical solution supplies a classical example for the elasticity theory.