Abstract: The fundamental theory presented in part(I) is used to analyze anisotropic plane stress problems.First we construct the generalized variational principle to enter Hamiltonian system and get Hamiltonian differential operator matrix;then we solve eigen problem;finally,we present the process of obtaining analytical solutions and semi-analytical solutions for anisotropic plane stress porblems on rectangular area.
Abstract: In this paper,we consider the upwind difference scheme for singular perturbation problem(1.1).On a special discretization mesh,it is proved that the solution of the upwind difference scheme is first order convergent,uniformly in the small parameter ε,to the solution of problem(1.1).Numerical results are finally provided.
Abstract: Using the Somigliana formula and the concepts of finite-part integral,a set of hypersingular integral equations to solve the arbitrary flat crack in three-dimensional elasticity is derived and its numerical method is then proposed by combining the finite-part integral method with boundary element method.In order to verify the method,several numerical examples are carried out.The results of the displacement discontinuities of the crack surface and the stress intensity factors at the crack front are in good agrement with the theoretical solutions.
Abstract: Model B-I for marco rectangular element is presented for the first time in this paper.To establish the influence surf ace for resultant R of bending plates,a number of generalized distributive loads q are defined.It is shown by numerical examples that Model B-I and the formula for the generalized distributive loads advanced in this paper are featured by high accuracy,low memory space and flexibility in practical application,and that they are especially effective for plate structures subject to moving loads,such as the two-dimensional continuous plates of highway bridges and the flat stabs in piled jetty engineering.
Abstract: In this paper by using tensor analysis we give the explicit expressions of the solution of the initial-value problem of homogeneous linear differential equations with constant coefficients and the nth-order homogeneous linear differential equation with constant coefficients.In fact,we give the general formula for calculating the elements of the matrix eAt.We also give the results when the characteristic equation has the repeated roots.The present method is simpler and better than the other methods.
Abstract: The transformations,which are similar to Mangler's transformations,are given in this paper.They change the entrance region flow of axially symmetrical laminar boundary layer between two parallel spherical surfaces into the flow of two-dimensional boundary layer,and simplify the problems.The simplified equations can be solved by the two-dimensional boundary layer theory and numerical methods.Therefore,a new way is opened up to solve the diffusive laminar flow in the entrance region between two parallel spherical surfaces.
Abstract: The bending of the thin elastic semicircular plates,because of its complicated boundary conditions,brings some difficulties for us to obtain its solution.This paper applies the reciprocal theorem to propose a general simple convenient method to obtain the transverse deflectional equations of the plates.
Abstract: In this paper,we propose some formulas for seeking a part of the particular solutions of the heavy harmonics and Tricomi equations and obtain the precise polynomial solutions of the finite-item number for rectangular strip bending problem when the intensity of the distributed load varies with the fourth power of longitudinal coordinate.
Abstract: In this paper,the driving forces at a pile top are considered as a periodic load during driving and the Mathieu equation is derived.From the stability charts of this equation,we can obtain the critical length of the pile,and the effect of skin friction upon the critical length is discussed.
Abstract: To begin with,in this paper,the displacement governing equations and the boundary conditions of nonsymmetrical large deflection problem of circular thin plates are derived.By using the transformation and the perturbation method,the nonlinear displacement equations are linearized,and the approximate boundary value problems are obtained.As an example,the nonlinear bending problem of circular thin plates subjected to comparatively complex loads is studied.
Abstract: In this paper,the elastic solutions of concentrated force acting in orthogonal anisotropic half-plane are derived by imaginal method and the formulae of coefficient matrix for constant element are put forward.To solve half-plane problems numerically by BEM,this paper provides the necessary formulae.Because the expressions of fundamental solutions are very simple,the object functions could be obtained for every integral of constant element and higher order element of indirect BEM.Thus,the procedure of integration could be avoided in calculation program