Analysis For Nonlinear Factors Of Steel Structures With Meshless Method

In advanced analysis of steel structures,the various nonlinear factors such as geometric nonlinearity,material nonlinearity,initial imperfection,residual stress, connection nonlinearity and second-order effect of member load etc.must be considered. At present,the finite element method is usually used in analysis of these nonlinear factors.However,there are some defects in the finite element analysis.For example,it is difficult to deal with modeling process.The problem is particularly serious in three-dimensional finite element analysis.When we deal with the grid adaptive calculation or simulation of crack growth,the modeling process becomes difficult.It makes the computational complexity and low computational accuracy.Therefore,we need a new numerical method,that is,meshless method.Meshless method is a new numerical method developed in the past two decades.In meshless method,a continuum is discretized into finite number of particles or nodes. Without the burden of meshing and element connectivity,meshless method has high continuity and flexible form.The pre-processing and post-processing are both simplified.And high accuracy is achieved in this method.Therefore,it can be widely applied to different complex engineering problems such as crack propagation problems, elasto-plastic analysis of materials,three-dimensional problems and so on.Meshless methods are better than the finite element methods in many aspects. Because the various nonlinear factors should be considered in advanced analysis of steel structures,meshless methods have wide application prospect and value.In this paper,by taking non-linear factors of steel structures as the subject for study and by using the finite-deformation theory of the nonlinear continuum mechanics and the meshless method,I do some work.The contents of this paper can be divided into six parts.1.By using of the least square,the element-free Galerkin method and penalty function method,the total lagrange and updated lagrange format discrete system equations of bar are obtained.The geometrical nonlinear stiffness matrix of bar and its relevant meshless method are derived.By using the finite-deformation theory of the nonlinear continuum mechanics and the element-free Galerkin method,a geometrical nonlinear stiffness matrix of beam-column and its relevant meshless method are obtained.The nonlinear stiffness matrix of beam-column with initial curvature and the total lagrange and updated lagrange format discrete system equations are obtained by using the least square and the element-free Galerkin method.In accordance with large deflection plate theory,the control equation of plate is obtained,which is used in geometrical nonlinear analysis of elastic thin plate.2.By using the total lagrange and updated lagrange format element-free Galerkin method,the coupling of the material nonlinearity and the geometrical nonlinearity is analyzed.The double nonlinear discrete system equation of beam-column is derived. Based on the double nonlinear analysis of beam-column,the geometrical imperfection is considered and the analysis of the material nonlinearity coupling with geometrical nonlinearity of beam-column with the geometrical imperfection is given by using the element-free Galerkin method.3.Aiming at the geometrical nonlinear factors and the connection nonlinear factors which effect beating capacity of steel structures,the meshless and finite element coupling method to semi-rigid steel frames is given by using the finite-deformation theory of the nonlinear continuum mechanics and the element-free Galerkin method.4.The geometrical nonlinear meshless equation of space bar member is established. The constraint condition has been introduced by using Lagrange multiplier method.The geometrical nonlinearity of space beam-column is analyzed by using total lagrange format element-free Galerkin method.By considering of the space thin walled beam structure with the axial force,bending,shear,restrained torsion,P-â–³effect,and warp, meshless geometric nonlinear method is established.The double nonlinear meshless analysis of the space thin walled beam structure is established by using whole format and increment format.5.The flow chart,main procedure of the main program and the subprogram are given.6.By contrasting the results of the finite element analysis and the experiment,the application and reliability of the method are verified.The influence factors such as the basic function,the weighting function,radius of influential domain and node density are discussed.The difference of the total lagrange and updated lagrange format element-free Galerkin method is contrasted.In a word,the aim of this paper is to establish an accurate and efficient new method to advanced analysis in nonlinear analysis of steel structures by using the meshless method.