• East Asian mathematical journal
• /
• v.37 no.5
• /
• pp.619-626
• /
• 2021

In [1, 2], we studied the string-like system with time-varying delay. Unlike the string system, the plate system must consider both longitudinal and transverse strains. First, we consider the physical phenomenon of an axially moving plate concerning kinetic energy, potential energy, and work dones. By the energy conservation law in physics, we have a nonlinear plate-like system with internal time delay.

• Structural Engineering and Mechanics
• /
• v.29 no.6
• /
• pp.623-642
• /
• 2008

While spatial plastic mechanism analysis has been widely and successfully applied to thinwalled steel structures to analyse the post-failure behaviour of sections and connections, there remains some contention in the literature as to the basic capacity of an inclined yield line. The simple inclined hinge commonly forms as part of the more complex spatial mechanism, which may involve a number of hinges perpendicular or inclined to the direction of thrust. In this paper some of the existing theories are compared with single inclined yield lines that form in flange outstands, by comparing the theories with plate tests of plates simply supported on three sides with the remaining (longitudinal) edge free. The existing mechanism theories do not account for different in-plane displacement gradients of the loaded edge, nor the slenderness of the plates, and produce conservative results. A modified theory is presented whereby uniform and non-uniform in-plane displacements of the loaded edge of the flange, and the slenderness of the flange, are accounted for. The modified theory is shown to compare well with the plate test data, and its application to flanges that are components of sections in compression and/or bending is presented.

• Structural Engineering and Mechanics
• /
• v.45 no.5
• /
• pp.677-691
• /
• 2013

A semi-analytical finite strip method is developed for analyzing the post-buckling behavior of rectangular composite laminated plates of arbitrary lay-up subjected to progressive end-shortening in their plane and to normal pressure loading. In this method, all the displacements are postulated by the appropriate harmonic shape functions in the longitudinal direction and polynomial interpolation functions in the transverse direction. Thin or thick plates are assumed and correspondingly the Classical Plate Theory (CPT) or Higher Order Plate Theory (HOPT) is applied. The in-plane transverse deflection is allowed at the loaded ends of the plate, whilst the same deflection at the unloaded edges is either allowed to occur or completely restrained. Geometric non-linearity is introduced in the strain-displacement equations in the manner of the von-Karman assumptions. The formulations of the finite strip methods are based on the concept of the principle of the minimum potential energy. The Newton-Raphson method is used to solve the non-linear equilibrium equations. A number of applications involving isotropic plates, symmetric and unsymmetric cross-ply laminates are described to investigate the through-thickness shearing effects as well as the effect of pressure loading, end-shortening and boundary conditions. The study of the results has revealed that the response of the composite laminated plates is particularly influenced by the application of the Higher Order Plate Theory (HOPT) and normal pressure loading. In the relatively thick plates, the HOPT results have more accuracy than CPT.