On the Reissner theory of bending of flastic plates

The Reissner equations of elastic plates are rederived on the bases of the incomplete generalized variational principle of Complementary energy. The Stress function is naturally obtained from the variational Calculation in the form of Lagrange multiplier. The stucture of solutions of the Reissner equations is thus defined. On the bases of these discussions, a simplified theory has been put forward, in which the equations of equilibrium involving the shearing influence can be reduced into a fourth order differential equation similar to those of the Classical theory of plates.     

The Dugdale model adapted to the transverse bending of plates

The Dugdale mathematical model is developed for the cylindrical bending of thin plates. The resulting finiteness condition, or plastic-zone size, is found to be a function of the applied moment and the normal coordinate of the plate. The results of cylindrical bending tests on polycarbonate are presented where plastic-zone size measurements are compared to the derived theoretical model. Good agreement is found although large deformations were encountered. The reasons for the validity of the theory as well as the good correlation between theory and experiment are discussed. Finally, compression plastic zones are presented and their relation to crack closure discussed.     

Uniqueness in the nonlinear dynamic bending of elastic plates

A uniqueness theorem for the solution of a nonlinear initial-boundary value problem for a time dependent form of von Karman's equations is proven. These equations are two coupled nonlinear fourth order partial differential equations which describe the bending of an elastic plate. The result is proved by the method of energy integrals.     

Influence of elastic support on the bending of parallelogram plates

Summary The influence of elastic support on the centre deflections and maximum centre and edge moments in clamped parallelogram shaped plates is examined. A polynomial series is assumed for the deflection function, and by applying Galerkin's process, an approximate solution to the governing differential equation is obtained. Convergence of the results were verified. Results for various skew angles and aspect ratios are presented graphically.Nomenclature 2a, 2b lengths of the sides of the parallelogram - a _mn undetermined parameter in series representing the deflection W - c = cosine - D flexural rigidity of plate =Eh ³/[12(1– ²)] - E Young's modulus - h thickness of plate - k, l, m, n, M, N positive integers - p aspect ratio = b/a - q intensity of uniform load - s = sine - u, v oblique co-ordinates - W lateral deflection - x, y Cartesian co-ordinates - reaction of foundation per unit area for unit deflection - adjustable constant, zero or one - outwardly drawn normal - , dimensionless oblique co-ordinates equal to v/b and u/a respectively - skew angle - Poisson's ratio     

General analytic solution for elastic bending of reissner plates

I.GeneralAnalyticSolutionforThickRectangularPlates1.1BasicequationsandboundaryconditionsTheoryofthewidelyusedReissuerplatesisquiteaccurateforengineeringcomputationand,asisshowninFig.l,ithasthefollowingassumDtionsfa)AthickrectangularplatewithmaterialpropertiesofelasticmodulusE,Poisson'sratiop,shearmodulusGanddimensionsofainlength,binw.idth.hinheightisconsiderd.anditsstrainsandstressescanbedescribledinthedeflectionofthemid-planeWandrotationsaroundx-axisandJ.-axisAandac,respectively.b)Thepl…     

On the dynamic bending of layered plates

The dynamic bending of layered metallic plates is studied. Their layers are reinforced with wires, and there are interfacial layers between the contact surfaces. A general approach to solving the corresponding dynamic problems is proposed. It is the principle of virtual work. A system of ordinary differential constitutive equations is obtained and used to determine the amplitude coefficients of the series of coordinate functions that approximates the deflections. The constitutive equations are reduced to Volterra equations of the second kind. Algorithms are developed to calculate the coefficients of the constitutive equations depending on the coordinate functions and on the reinforcement pattern. Possible methods to set up coordinate functions and solve integral equations are indicated     

Rational finite element method for elastic bending of reissner plates

IntroductionAsawell-establishedandsophisticatednumericalanalysistechniqueforthedifferentialequahons,thefiniteelementmethodwasoriginatedindependentlybythedomesticandtheforeignmechanicalinvestigatorstheyyearsago.ItfoundforthefirsttimewideapplicationsintheelasticstfUctolproblemsandwiththedevelopmentofcomputerextendedinvaryingdegreestOalmostalltheengineeringdisciplinesandmanyscientificandtechnologicalfields.Thisleadstoadramaticbreakthroughforthecurrentcomputationalmathematics.Themathematicalbasis…