An element free Galerkin method for the free vibration analysis of composite laminates of complicated shape

• Published in: Composite structures Vol. 59; no. 2; pp. 279 - 289
• Main Authors: Chen, X.L., Liu, G.R., Lim, S.P.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01-02-2003; Elsevier Science
• Subjects: Applied sciences; Composites; Computational techniques; Eigenvalue analysis; Element free Galerkin method; Exact sciences and technology; Forms of application and semi-finished materials; Fundamental areas of phenomenology (including applications); Laminates; Mathematical methods in physics; Numerical analysis; Physics; Polymer industry, paints, wood; Solid mechanics; Structural and continuum mechanics; Technology of polymers; Vibration; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Vibrations and mechanical waves; Element free Galerkin method; Eigenvalue analysis; Vibration; Numerical analysis; Laminates; Lagrangian; Stratified material; Free vibration; Numerical method; Composite material; Orthogonal transformation; Natural frequency; Lagrange multiplier; Weak solution; Least squares method; Elliptic plate; Meshless method; Rectangular plate; Galerkin method; Eigenvalue problem; Structural analysis
• ISSN: 0263-8223; 1879-1085
• DOI: 10.1016/S0263-8223(02)00034-X

An element free Galerkin (EFG) method is proposed to analyze the natural frequencies of composite laminates of complicated shape. The present method uses moving least squares (MLS) approximation to construct shape functions based on a set of nodes scattered in the problem domain. The dynamic equations of the system are formulated using the Lagrangian equation. The essential boundary conditions are imposed using their weak forms with Lagrange multipliers. Orthogonal transformation technique is used to implement the essential boundary conditions in the eigenvalue equation. The present EFG method is coded in Fortran. Numerical examples are presented for plates of square, elliptical and complicated shapes with different boundary conditions.