Residual energy balancing technique in the generation of plate bending finite elements

Abstract The residual shear balancing technique of Refs [1 and 2] is discussed and applied to the generation of the stiffness matrix of a 12 degree-of-freedom rectangular plate bending element. Numerical results both in statics and dynamics are compared with those obtained with elements of similar size.

[1]  Theodore H. H. Pian,et al.  Finite Element Methods in Continuum Mechanics , 1972 .

[2]  Garrett Birkhoff,et al.  Smooth Surface Interpolation , 1960 .

[3]  J. A. Stricklin,et al.  A rapidly converging triangular plate element , 1969 .

[4]  S. Atluri,et al.  An assumed stress hybrid finite element model for linear elastodynamic analysis. , 1973 .

[5]  J. S. Przemieniecki Matrix methods in structural mechanics , 1966 .

[6]  William Prager Variational principles for elastic plates with relaxed continuity requirements , 1968 .

[7]  Garry M. Lindberg,et al.  Convergence studies of eigenvalue solutions using two finite plate bending elements , 1970 .

[8]  W. Visser A refined mixed-type plate bending element. , 1969 .

[9]  T. Pian Derivation of element stiffness matrices by assumed stress distributions , 1964 .

[10]  S. Kelsey,et al.  Triangular Plate Bending Elements with Enforced Compatibility , 1970 .

[11]  I. Fried,et al.  Shape functions and the accuracy of arch finite elements. , 1973 .

[12]  R. T. Severn,et al.  Vibration of plate and shell structures using triangular finite elements , 1967 .

[13]  R. W. Mclay A special variational principle for the finite element method. , 1969 .

[14]  B. Tabarrok,et al.  A variational principle for the dynamic analysis of continua by hybrid finite element method , 1971 .

[15]  Isaac Fried,et al.  Shear in C0 and C1 ending finite elements , 1973 .

[16]  Leonard R. Herrmann,et al.  Finite-Element Bending Analysis for Plates , 1967 .

[17]  Isaac Fried,et al.  Triangular, nine-degrees-of-freedom, $C^0$ plate bending element of quadratic accuracy , 1973 .

[18]  T. H. H. Pian,et al.  Application of the smooth-surface interpolation to the finite-element analysis. , 1967 .

[19]  R. P. Nordgren,et al.  A bound on the error in plate theory , 1971 .

[20]  Isac Fried,et al.  Bounds on the spectral and maximum norms of the finite element stiffness, flexibility and mass matrices , 1973 .

[21]  T. Pian,et al.  On the convergence of the finite element method for problems with singularity , 1973 .