An Accurate Solution Method for the Static and Vibration Analysis of Functionally Graded Reissner-Mindlin Rectangular Plate with General Boundary Conditions

This paper presents an accurate solution method for the static and vibration analysis of functionally graded Reissner-Mindlin plate with general boundary conditions on the basis of the improved Fourier series method. In the theoretical formulations, the governing equations and the general elastic boundary equations are obtained by using Hamilton’s principle. The components of admissible displacement functions are expanded as an improved Fourier series form which contains a 2D Fourier cosine series and auxiliary function in the form of 1D series. The major role of the auxiliary function is to remove the potential discontinuities of the displacement function and its derivatives at the edges and ensure and accelerate the convergence of the series representation. The characteristic equations are easily obtained via substituting admissible displacement functions into governing equations and the general elastic boundary equations. Several examples are made to show the excellent accuracy and convergence of the current solutions. The results of this paper may serve as benchmark data for future research in related field.

A new displacement bound technique for rigid plastic continua subjectet to strong dynamic loading at large deflections II.

The method developed in [ 1] is applied herein in order to obtain lower hound to large displacements of the hinge supported circular plate acted on by impulsively, uniformly distributed loading. The plate is made from rigid and perfectly plastic material which yields according to the yield condition shown in fig- 1· The lower bound (1.21) is obtained when the dynamically admissible displacement and velocity are chosen in separated variable form which is a scalar time function multiplied by a vector shape function of space variable (1.13). In the case when W, Ẇ * are chosen in form (1.22). [comparison of the obtained estimate Eq (1.24) with previous solution of the same problem [1], upper bound [2] and experimental date [3] are presented in fig. 2

A new displacement bound technique for rigid plastic continua subjected to strong dynamic loading at large deflections

A new displacement bound technique, which is based on concept of admissible fields has been developed for rigid Plastic continua subjected to strong dynamic loading at large deflections, the lower hound obtained (2.11) depends on kinematic ally admissible displacement ui and kinematic ally admissible velocity ui* which must be chosen so that the condition (2.14) may be satiafidc. Parameter T* would be determinated by maximizing the right hand side of (2.11).

A Displacement Bound Principle for Inelastic Continua Subjected to Certain Classes of Dynamic Loading

The paper presents an inequality relating statically admissible stress fields and kinematically admissible displacement fields for continua composed of inelastic materials which obey a postulated criterion of stability. The inequality is used to compute displacement bounds for inelastic continua subjected to certain classes of dynamic loading.