Von Karman Nonlinear Theory Research Articles

Refined buckling and postbuckling analysis of two-dimensional delaminations—I. analysis and validation

An analytical procedure, based on the Rayleigh-Ritz method and von Karman's nonlinear theory of plates, is developed for computing the buckling loads and the postbuckling solutions of laminated anisotropic elliptical plates. Lengthy algebraic equations governing the expansion coefficients of the displacement functions are generated by a symbolic algorithm. Using polynomial displacement expansions of different orders, postbuckling solutions with increasing accuracy are systematically computed for isotropic and laminated elliptical plates. The deflections, the force and moment resultants and the energy release rates associated with the solutions of various orders arc compared to assess the trend of convergence. The comparison suggests the lowest order polynomial expansion needed to obtain reasonably accurate results for the force and moment resultants and the energy release rates. Previous Rayleigh-Ritz postbuckling solutions based on lower-order polynomial expansions of the displacements are found to yield results with significant errors.

Orthotropic von Karman plates using higher order elements

The nonlinear behaviour of orthotropic plates subject to transverse loading is studied in this paper using higher order finite elements. The formulation procedure for elements with up to 25 nodes is established and derivation of the tangential stiffness matrix based on the classical von Karman nonlinear theory is presented. These elements are derived by employing a high order polynomial displacement function to represent the in-plane and the bending displacements. By adopting separate variables for the transverse deflections and the rotations of the plate, the effect of transverse shear deformation can be included in modelling thin to moderately thick plates, thus enabling the effect of transverse shear on the nonlinear behaviour of plates to be included. The Newton-Raphson method for solving nonlinear equations is adopted to obtain the final state of equilibrium of the system. Several numerical examples are presented and the results are compared with available experimental data as well as analytical and numerical solutions obtaned by other conventional methods. Satisfactory agreement on the nonlinear performance of the plates as predicted by the present method is demonstrated.

Higher order subparametric elements for large deflection analysis of plates

A family of higher-order subparamctric elements has been developed for large deflection analysis of flat plates of any geometric shapes subjected to lateral loading. The formulation procedure for these elements with 17–25 nodes involving in-plane as well as bending displacements with subparametric transformation is described and the derivation of the tangential stiffness matrix based on the classical von Karman nonlinear large deflection theory is presented. The Newton-Raphson scheme with modification is used. Several numerical examples of skewed slabs and circular plates are worked out and the results are compared with available data given by other research workers. It is found that these higher-order elements are simple, versatile, economical and convenient to use and give accurate results for large deflection analysis of plates.

Postbuckling behaviour of hardboard under shear

The purpose of the study was to analyse the postbuckling behaviour of hardboard under shear both experimentally and theoretically. Two series of 400 mm x 400 mm x 3.2 mm and 400 mm x 400 mm x 4.0 mm hardboard were tested experimentally in the special apparatus which was supposed to satisfy the boundary and load conditions. During increasing shear load, the hardboard deformations were measured in order to determine the first and second critical loads and the failure load. The experimental results were compared with the numerical solution based on the von Karman nonlinear theory of plates. A good agreement of experimental results with theoretical solution was achieved.