Development and application of assumed strain smoothing finite element technique for composite plate/shell structures

Development and application of assumed strain smoothing finite element technique for composite plate/shell structures

The present study is mainly concerned with the development and application of simple, efficient and accurate finite element models for geometrically linear and nonlinear analysis of composite plates/shells. It is also demonstrated that the developed approach can be extended for analysis of functionally graded material (FGM) structures as well as coupled electric-structural piezoelectric systems.

The primary goal is achieved through the development of two novel four-node displacement-based Co quadrilateral flat elements, one with fictional drilling DOFs
(MISQ20) and one with actual drilling DOFs (MISQ24) within the framework of the first-order shear deformation theory (FSDT). The developed elements are based on the incorporation of the strain smoothing technique of the stabilized conforming nodal integration (SCNI) mesh-free method into the four-node quadrilateral finite elements. The most distinguishing feature of the present elements is the evaluation of membrane, bending and geometric stiffness matrices by integration along the boundary of smoothing elements. It is observed that this assumed strain
smoothing technique can yield more accurate solutions even with badly shaped elements or coarse discretization and reduce computational time when compared with domain integration approach. To accommodate small strain geometric nonlinearity with large deformations, the von-Karman's large deflection theory and the total Lagrangian approach are employed to formulate the present elements
for geometrically nonlinear analysis. The present formulation is therefore applicable to moderately thick and thin plate/shell configurations, involving isotropic or
composite material properties, with improved solutions in a wide range of geometrically linear and nonlinear problems. Extensive numerical verification is carried
out with a set of demanding benchmark problems and the present results are compared with analytical, experimental and numerical solutions in the literature. The comparative study does show the validity as well as the high-performance of the developed finite element models for laminated composite structures. The developed approach also performs very well in the analysis of FGM plate structures under thermo-mechanical loading.

The analysis of coupled mechanical-electrical behaviours of piezoelectric problems is accomplished by the normalization of both mechanical strains and electric
potential fields using the smoothing constant function of the SCNI. Two novel piezoelectric elements for linear static and free vibration analysis of planar piezo-
electric structures are proposed. The first one, the cell-based element (SPQ4), is based on the subdivision of original quadrilateral finite elements into smoothing cells. The second one, the node-based element (NSPE-T3 or NSPE-Q4), is created by transforming a triangular or quadrilateral mesh into a mesh of new smoothing cells associated with each of the nodes of the original mesh. The reliability and accuracy of the proposed formulations are demonstrated through various favourable comparisons with other existing elements and analytic solutions. The
present models are attractive for coupled multifield problems owing to the following properties: (i) very good accuracy, (ii) insensitivity to mesh distortion, and
(iii) simplicity of formulation.