Analysis of critical imposed load of plate using variational calculus

This work studied the critical load analysis of rectangular plates, carrying uniformly distributed loads utilizing direct variational energy calculus. The aim of this study is to establish the techniques for calculating the critical lateral imposed loads of the plate before deflection attains the specified maximum threshold, qiw as well as its corresponding critical lateral imposed load before the plate reaches an elastic yield point. The formulated potential energy by the static elastic theory of the plate was minimized to get the shear deformation and coefficient of deflection. The plates under consideration are clamped at the first and second edges, free of support at the third edge and simply supported at the fourth edge (CCFS). From the numerical analysis obtained, it is found that the critical lateral imposed loads (qiw and qip) increase as the thickness (t) of plate increases, and decrease as the length to width ratio increases. This suggests that as the thickness increases, the allowable deflection improves the safety of the plate, whereas an increase in the span (length) of the plate increases the failure tendency of the plate structure.

A fundamental class of stress elements in lower bound limit analysis

There is a major restriction in the formulation of rigorous lower bound limit analysis by means of the finite-element method. Once the stress field has been discretized, the yield criterion and the equilibrium conditions must be applied at a finite number of points so that they are satisfied everywhere throughout the discretized structure. Until now, only the linear stress elements fulfil this requirement for several types of loads and structural conditions. However, there are also standard types of problems, like the one of plates under uniformly distributed loads, where the implementation of the lower bound theorem is still not possible. In this paper, it is proven for the first time that there is a class of stress interpolation elements which fulfils all the requirements of the lower bound theorem. Moreover, there is no upper restriction of the polynomial interpolation order. The efficiency is examined through plane strain, plane stress and Kirchhoff plate examples. The generalization to three-dimensional and other structural conditions is also straightforward. Thus, this interpolation scheme which is based on the Bernstein polynomials is expected to play a fundamental role in future developments and applications.

Modeling the dynamic bending of rigid-plastic fiber-reinforced laminated curvilinear doubly connected thin plates with free outer contour

A theoretical model of the dynamic bending of rigid-plastic hybrid composite, arbitrary curvilinear doubly connected thin plates is developed. Inner contour of the plate is simply supported or clamped and outer one is free. The plates are on a viscous basis and under the action of uniformly distributed loads of explosive type. The plates are laminated and fibrous, with layers arranged symmetrically with respect to the middle surface. In each layer the reinforcing fibers, made of different materials, are located in directions parallel or normal to inner contour of plate. The structural model of the reinforced layer considering the plane stress state in fibers is used. The equations of the dynamic deformation of plate and simple analytical formula for the limit load are obtained. Numerical examples are given for a fiber-reinforced four-layered curvilinear plate with a supported hole in the form of ellipse and super-ellipse at the same total amount of reinforcement.

Fire Resistance of Composite Beams with Restrained Superposed Slabs

To investigate the fire resistance of composite beams with restrained superposed slabs, three specimens were tested under uniformly distributed loads in a furnace. The effects of the thickness of the postcast top layer in superposed slabs and the spacing of shear studs on the structural behaviours of composite beams under fire were further examined. During the tests, the temperature distributions of the superposed slabs and steel beams as well as the displacements at their key positions were recorded and analysed. It was found that the temperature of the concrete superposed slabs decreased long their heights from the bottom. The most drastic change of the temperature along the slab cross section was found in the region with a distance of 40 mm to the slab bottom. The concrete superposed slabs could impose restraints to the steel beams due to their incompatible deformations. Cracks were developed on the top surfaces of the specimens and the superposing interfaces between the precast slabs and postcast top layers were not broken. Through the comparisons of different specimens, the spacing of shear studs could have a significant effect on the fire resistance of composite beams, especially for their deformation recovery capacities. In contrast, the effect of the thickness of the postcast top layers was negligible. ABAQUS was employed to simulate the temperature fields and deformation behaviours of composite beam specimens based on a sequenced thermomechanical coupling analysis. The numerical results agreed well with the experiment data, which validated the developed numerical model.