Influence of shear deformation in a composite equilibrium element for the analysis of thin plates

A composite triangular equilibrium element for modelling thin plate behaviour is investigated when shear deformation, according to Reissner's theory, is included in addition to bending deformation. The element flexibility matrix is formed as the sum of two component matrices containing the contributions from piecewise linear moment fields and piecewise constant shear fields separately. Properties of the shear component matrix, including its rank, are determined, and the influence of load basis on the pattern of this matrix is studied. The way these properties affect the condition of a flexibility matrix is investigated when the element size/thickness ratio varies, and particularly when this ratio tends towards zero. Load bases are suggested which could avoid certain problems of ill‐conditioning. Condition parameters are evaluated for an equilateral element. Finally, the application of kinematic boundary conditions to the equilibrium is considered.