The enhanced assumed strain (EAS) method, recently proposed by Simo and Rifai13, is used to develop new four-node membrane, plate and shell elements and eight-node solid elements. The equivalence of certain EAS-elements with Hellinger-Reissner (HR) elements is discussed. For instance, the seven-parameter element EAS-7 with 2 × 2 integration is identical to the HR-element of Pian and Sumihara2. Eight-node solid elements which are free of volumetric locking and four-node shell elements which have an improved membrane and bending behaviour, compared to the Bathe-Dvorkin shell element7, are introduced. Numerical tests for linear elastic problems show an improved performance of the EAS-elements.

EAS‐elements for two‐dimensional, three‐dimensional, plate and shell structures and their equivalence to HR‐elements

A new approach for choosing the stress terms for hybrid stress elements is based on the condition of vanishing of the virtual work along the element boundary due to the stress terms higher than constant and the additional incompatible displacements. Examples using 4-node plane stress elements have shown that when the incompatible displacements also satisfy the constant strain patch test the resulting element will provide the most accurate solutions.

A rational approach for choosing stress terms for hybrid finite element formulations

Use of incompatible displacement modes for the calculation of element stiffnesses or stresses

SUMMARY An improved plane strain/stress element is derived using a Hu-Washizu variational formulation with bilinear displacement interpolation, seven strain and stress terms, and two enhanced strain modes. The number of unknowns of the four-node element is increased from eight to ten degrees of freedom. For linear and non-linear applications, the two unknowns associated with the enhanced strain terms can be eliminated by static condensation so that eight displacement degrees of freedom remain for the proposed element, which is denoted by QE2. The excellent performance of the proposed element is demonstrated using several linear and non-linear examples.

A Quadrilateral Mixed Finite Element with Two Enhanced Strain Modes

http://hub.hku.hk/bitstream/10722/54309/1/49011.pdf

Hybrid finite element models for piezoelectric materials

Consistency condition and convergence criteria of incompatible elements: general formulation of incompatible functions and its application

Boundary element analysis of shallow shells involving shear deformation

Large deflections of rectangular hoff sandwich plates

Computation of the fundamental solution for shallow shells involving shear deformation

Postbuckling behavior is investigated for Rectangular Reissner's moderately thick plates and sandwich plates. The fundamental equations and boundary conditions are expressed in unified dimensionless form for rectangular moderately thick plates and sandwich plates. Exact solutions of series form with a number of different boundary conditions, especially with unsymmetrical boundary conditions, are obtained by developing a new technique of mixed Fourier series in nonlinear analysis. The nonlinear partial differential equations are reduced to an infinite set of simultaneous nonlinear algebraic equations, which are truncated by iteration in numerical computations.

Huang Mao-guang

Papers

Consistency condition and convergence criteria of incompatible elements: general formulation of incompatible functions and its application

Boundary element analysis of shallow shells involving shear deformation

Large deflections of rectangular hoff sandwich plates

Computation of the fundamental solution for shallow shells involving shear deformation

POSTBUCKLING BEHAViOR OF RECTANGULAR MODERATELYTHICK PLATES AND SANDWICH PLATES