Beam elements based on a higher order theory—I. Formulation and analysis of performance

The flexure of deep beams, thick plates and shear flexible (e.g. laminated composite) beams and plates is often approached through a finite element formulation, based on the Lo-Christensen-Wu (LCW) theory. This paper is a systematic analytical evaluation of the use of the LCW higher order theory for finite element formulation. The accuracy and other features of the computational model are evaluated by comparing finite element method (FEM) results with available closed form classical and elasticity solutions. Wherever possible, errors are predicted by an a priori analysis using these solutions and concepts from an understanding of what the finite element method does.

[1]  Rakesh K. Kapania,et al.  Recent advances in analysis of laminated beams and plates. Part I - Sheareffects and buckling. , 1989 .

[2]  R. D. Mindlin,et al.  Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates , 1951 .

[3]  Ozden O. Ochoa,et al.  Through‐the‐thickness stress predictions for laminated plates of advanced composite materials , 1985 .

[4]  C. T. Sun,et al.  A three-dimensional hybrid stress isoparametric element for the analysis of laminated composite plates , 1987 .

[5]  R. Christensen,et al.  Stress solution determination for high order plate theory , 1978 .

[6]  Higher-order theories for symmetric and unsymmetric fiber reinforced composite beams with C 0 finite elements , 1990 .

[7]  Gangan Prathap,et al.  Beam elements based on a higher order theory-II - Boundary layer sensitivity and stress oscillations , 1996 .

[8]  Rakesh K. Kapania,et al.  Recent Advances in Analysis of Laminated Beams and Plates, Part II: Vibrations and Wave Propagation , 1989 .

[9]  B. D. Agarwal,et al.  Analysis and Performance of Fiber Composites , 1980 .

[10]  Robert L. Spilker,et al.  Hybrid-stress eight-node elements for thin and thick multilayer laminated plates , 1982 .

[11]  M. Levinson,et al.  An accurate, simple theory of the statics and dynamics of elastic plates , 1980 .

[12]  G. Prathap.  The Finite Element Method in Structural Mechanics , 1993 .

[13]  B. S. Manjunatha,et al.  Different Numerical Techniques for the Estimation of Multiaxial Stresses in Symmetric/Unsymmetric Composite and Sandwich Beams with Refined Theories , 1993 .

[14]  P. Mohan,et al.  Consistent and variationally correct finite elements for higher-order laminated plate theory , 1994 .

[15]  O. C. Zienkiewicz,et al.  A refined higher-order C° plate bending element , 1982 .

[16]  J. N. Reddy.  A review of the literature on finite-element modeling of laminated composite plates , 1985 .

[17]  S. Tsai,et al.  Introduction to composite materials , 1980 .

[18]  E. Reissner.  The effect of transverse shear deformation on the bending of elastic plates , 1945 .