LARGE DEFLECTION AND INITIAL INSTABILITY ANALYSIS OF ANISOTROPIC PLATES BY THE GENERALIZED FINITE ELEMENT METHOD

Abstract

THIS PAPER PRESENTS INVESTIGATIONS CONCERNING MODERATELY LARGE TRANSVERSAL PLATE DISPLACEMENTS AND ITS INITIAL INSTABILITY IN LAMINATED PLATES THROUGH THE GENERALIZED FINITE ELEMENT METHODS, GFEM. HERE, THE VON KÁRMÁN PLATE HYPOTHESIS ARE USED ALONG WITH KIRCHHOFF AND REISSNER-MINDLIN KINEMATIC PLATE MODELS TO APPROXIMATE TRANSVERSE DISPLACEMENTS AND CRITICAL BUCKLING LOADS. THE GENERALIZED APPROXIMATION FUNCTIONS ARE EITHER C0 OR CK CONTINUOUS FUNCTIONS, WITH K BEING ARBITRARILY LARGE. IT IS WELL KNOWN THAT IN GFEM, WHEN BOTH THE PARTITION OF UNITY (POU) AND THE ENRICHMENTS FUNCTIONS ARE POLYNOMIALS, THE STIFFNESS MATRICES ARE SINGULAR OR ILL CONDITIONED, WHICH CAUSES ADDITIONAL DIFFICULTIES IN APPLICATIONS THAT REQUIRES THE SOLUTION OF ALGEBRAIC EIGENVALUES PROBLEMS, LIKE IN THE DETERMINATION OF NATURAL FREQUENCIES OF VIBRATION AND INITIAL BUCKLING LOADS. SOME INVESTIGATIONS REGARDING THIS PROBLEM ARE PRESENTLY ADDRESSED AND SOME ASPECTS AND ADVANTAGES OF USING CK-GFEM ARE OBSERVED. IN ADDITION, COMPARISONS ARE PRESENTED BETWEEN THE CLAS-SICAL GFEM AND THE STABLE-GFEM (SGFEM) WITH REGARD TO THE EVALUATION OF THE INITIAL CRITICAL BUCKLING LOADS. THE NUMERICAL EXPERIMENTS USE REFERENCE VALUES FROM ANALYTICAL AND NUMERICAL RESULTS OBTAINED IN THE OPEN LITERATURE.