Stress-based hierarchic models for laminated composites

Abstract Derivation of hierarchic sequence of equilibrium models for cylindrical bending of composite laminates is presented. The levels of hierarchy correspond to the degree to which the second-order compatibility equation of the two-dimensional elasticity is satisfied. The stress fields of the hierarchic models satisfy a priori the equilibrium equations and the stress boundary conditions of two-dimensional elasticity, and the continuity requirements for the transverse shear and normal stresses at the lamina interfaces are also a priori satisfied for each member of the hierarchy. The numerical solution is based on the principle of minimum complementary energy. The number of degrees of freedom in the finite element approximation is independent of the numbers of the layers in the laminate. The results are obtained directly for stresses, whereas the displacements are calculated in the post-processing phase, by integration. Numerical results with comparisons present the performance of the mathematical and numerical models proposed.

[1]  I. Babuska,et al.  Finite Element Analysis , 2021 .

[2]  E. Berto´ti.  Complementary energy method for cylindrical shells using second order stress functions , 1993 .

[3]  Barna A. Szabó,et al.  Hierarchic plate and shell models based on p-extension , 1988 .

[4]  K. Washizu.  Variational Methods in Elasticity and Plasticity , 1982 .

[5]  I. Babuska,et al.  Locking effects in the finite element approximation of elasticity problems , 1992 .

[6]  R. Actis,et al.  Hierarchic models for bidirectional composites , 1993 .

[7]  A finite element model for plane elasticity problems using the complementary energy theorem , 1982 .

[8]  Juhani Pitkäranta,et al.  On the membrane locking of h-p finite elements in a cylindrical shell problem , 1994 .

[9]  I. Babuska,et al.  Hierarchic models for laminated composites , 1992 .

[10]  Ivo Babuška,et al.  Hierarchic modeling of plates , 1991 .

[11]  K. Chandrashekhara,et al.  Recent Advances in the Nonlinear Analysis of Laminated Composite Plates and Shells , 1987 .

[12]  Michel Fortin,et al.  Mixed and Hybrid Finite Element Methods , 2011, Springer Series in Computational Mathematics.

[13]  Ahmed K. Noor,et al.  Assessment of computational models for multilayered composite cylinders , 1991 .

[14]  Finite element structural analysis and complementary energy , 1993 .

[15]  D. Arnold.  Mixed finite element methods for elliptic problems , 1990 .

[16]  I. Babuska,et al.  Locking effects in the finite element approximation of plate models , 1995 .

[17]  Ahmed K. Noor,et al.  Assessment of Shear Deformation Theories for Multilayered Composite Plates , 1989 .

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

[19]  R. H. Gallagher,et al.  Direct Flexibility Finite Element Elastoplastic Analysis , 1971 .

[20]  I. Babuska,et al.  On locking and robustness in the finite element method , 1992 .

[21]  N. Pagano,et al.  Exact Solutions for Composite Laminates in Cylindrical Bending , 1969 .

[22]  J. H. Argyris,et al.  Energy theorems and structural analysis , 1960 .

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

[24]  Ivo Babuška,et al.  The p-Version of the Finite Element Method for Parabolic Equations. Part 1 , 1981 .