BENDING SOLUTION OF A RECTANGULAR PLATE WITH ONE EDGE BUILT－IN AND ONE CORNER POINT SUPPORTED SUBJECTED TO UNIFORM LOAD

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一边固定一角点或二角点支承的矩形板弯曲统一求解方法

本文的统一法可以解决悬壁板或带有角点支承时在任意荷载作用下的弯曲。这种方法求解思路清晰、收敛速度快,计算精度高。     

Bending of uniformly loaded rectangular plates with two adjacent edges clamped, one edge simply supported and the other edge free

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The bending of a thick rectangular plate with three clamped edges and one free edge

The exact solution of the bending of a thick rectangular plate with three clamped edges and one free edge under a uniform transverse load is obtained by means of the concept of generalized simply-supported boundary^[1] in Reissner’s theory of thick plates. The effect of the thickness h of a plate on the bending is studied and the applicable range of Kirchhoffs theory for bending of thin plates is considered.     

The bending of set squares with one free oblique edge under a concentrated load

I-Introduction-Itisveryimportanttoresearchonthebendingofelasticthinplateinpractice.Alotofworkaboutthisproblemhavebeendonebythescholarsandexpertsofmanycountriesintheworld.However.therearefewpeoplewhostudied-thebendingofsetsquareundervarioussupportsandloads…     

Stresses in square slabs,with different edge geometries,when bonded on one face to a rigid plate and shrunk

An approximately square epoxy slab (≈14 in. ×≈14 in. ×1 in.) with four different edge geometries was bonded to a rigid plate on one of its faces. In the process of “freezing” photoelastic effects, a state of restrained shrinkage developed. Slices removed from the slab were used to determine the concentration factors corresponding to the four geometries.     

Suppression of edge cracking in layered ceramic composites by edge coating

A strategy is proposed to reduce surface tensile stresses that develop in ceramic microlaminate structures. As a specific example, surface stresses, which can lead to unwanted edge cracking, appear within a thin alumina/mullite layer bounded by thicker alumina layers after fabrication at some elevated temperature and subsequent cooling. A stress analysis is performed using the finite element method on a geometry in which the (edge) surface of the ceramic sandwich structure has been coated with an overlayer of the alumina/mullite material with thickness proportional to the initial buried layer thickness. These analyses show there is a critical thickness of the overlayer at which the surface tensile stresses can be reduced to zero. Stress concentration factors are calculated numerically for cracks propagating through this structure, and thus the resistance to surface cracking is quantified.     

The nonuniformly moving edge dislocation

The motion of an edge dislocation starting from rest and moving thereafter nonuniformly on its slip-plane is analyzed by means of Laplace transforms in space and time, with detailed treatment of the singularities involved. The stress and particle velocities are derived in the form of an integral over the history of the motion in the case of a general motion and in closed form in the special case of a dislocation starting from rest and moving with constant velocity thereafter.     

Bifurcations of heterodimensional cycles with one orbit flip and one inclination flip

In this paper, the bifurcations of heterodimensional cycles are investigated by setting up a suitable local coordinate system in a four-dimensional system. Under some ungeneric conditions—one orbit flip and one inclination flip—the persistence of heterodimensional cycles, the existence of homoclinic orbit and a family of periodic orbits, the coexistence of heterodimensional loop and periodic orbit are obtained. Also, the relevant bifurcation surfaces and their existing regions are given.     

Elastic interaction between edge dislocation,concentrated force,point heat source and edge crack in a semi-infinite plane

We investigate the interaction between edge crack and edge dislocation as well as concentrated force and point heat source. The stress intensity factors at the edge crack tip and the image forces acting on the edge dislocation are calculated. The influence of the concentrated force, point heat source and edge dislocation on the shielding and anti-shielding effects to edge crack as well as the glide and climb forces acting on the edge dislocation is examined in detail. The results indicate that the shielding and anti-shielding effects increase acutely with the increment of concentrated force and point heat source. In addition, the glide and climb forces increase acutely with the decrement of the distance between dislocation and crack tip.     

Numerical simulation of loading edge cracks by edge impact using the extended finite element method

The extended finite element method is used to analyze a plate with two parallel edge cracks impacted by a cylindrical projectile. The influence of the impact speed, crack length,plate thickness and notch tip radius on the crack initiation and propagation is studied. Dynamics equations are solved by an implicit time integration scheme which is unconditionally stable. Very good agreement is achieved between numerical predictions and experimental results. The critical velocity of the crack initiation under different conditions is examined. The influence of the crack length is greater than that of the impact speed, plate thickness and notch tip radius.     

The edge dislocation in a three-quarter plane. Part II: Application to an edge crack

This paper presents the solution for the crack tip stress intensity factors for a short crack emanating from the corner of a three-quarter plane. The solution employs the influence functions for a dislocation along one of the projection lines of a three-quarter plane together with the Williams semi-infinite wedge solutions, and the result is valid for any remote loading configuration. The sole proviso is that the crack is short enough to be considered well within the region in which the asymptotes govern the stress state. This general solution is then applied to a specific geometry and is compared with a calibration for the stress intensity factors for a similar geometry.     

Nonlinear effects on edge wave development

The effect of nonlinearity on the evolution of free edge waves is investigated by solving numerically the nonlinear shallow water equations. The numerical scheme is the two-dimensional WAF method, originally developed by Toro [Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer, 1997]. First, a simple beach geometry [J. Fluid Mech. 381 (1999) 271] is considered and the numerical results are validated against available analytical solutions for small amplitude edge waves. Then, results are obtained for edge waves of larger amplitude. Nonlinear effects are found to be relevant even for moderate values of the nonlinearity parameter a which is the ratio between the wave amplitude and the water depth. In particular a resonance phenomenon has been observed which causes a modulation in time of the ultra-harmonic components of the wavefield. Larger values of a lead to a complex time evolution.