High-order plate bending analysis based on the scaled boundary finite element method

• Published in: International journal for numerical methods in engineering Vol. 95; no. 4; pp. 331 - 360
• Main Authors: Man, H., Song, C., Xiang, T., Gao, W., Tin-Loi, F.
• Format: Journal Article
• Language: English
• Published: Chichester Blackwell Publishing Ltd 27.07.2013; Wiley; Wiley Subscription Services, Inc
• Subjects: Bending; Boundaries; Computational techniques; Exact sciences and technology; Finite element method; Finite-element and galerkin methods; Fundamental areas of phenomenology (including applications); Mathematical analysis; Mathematical methods in physics; Mathematical models; Mathematics; Methods of scientific computing (including symbolic computation, algebraic computation); Numerical analysis. Scientific computation; Padé expansion; Physics; plate bending; plate structures; Reproduction; scaled boundary finite element method; Sciences and techniques of general use; Solid mechanics; spectral elements; Static elasticity (thermoelasticity...); Stiffness matrix; Structural and continuum mechanics; Three dimensional; Stiffness matrix; Moderately thick wall; Thin plate; Curved plate; Thick plate; Padé expansion; Modeling; plate bending; Finite element method; spectral elements; plate structures; Convergence rate; Spectral element method; Padé approximant; scaled boundary finite element method; Structural analysis; Locking
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.4519

SUMMARY This paper presents a technique for plate bending analysis based on the scaled boundary FEM. The proposed technique is formulated directly from the three‐dimensional governing equations. The in‐plane dimensions of the plate are modelled by two‐dimensional finite elements. The solution along the thickness is expressed analytically as a Padé expansion by using the scaled boundary FEM. A simple and highly efficient procedure to construct the stiffness matrix of a thin to moderately thick plate element is devised. Furthermore, the use of high‐order spectral elements allows the proposed technique to accurately handle plates with curved boundaries and leads to high accuracy and convergence rate. Five plate bending problems are presented with results showing high computational efficiency. No numerical locking arises. Copyright © 2013 John Wiley & Sons, Ltd.