Refined Finite Element Method For Grid Structures

Different finite element models of the grid strctures can affect the analysis accuracy of analysis greatly. If the pipes and joints in the grid structure are all discreted by fine solid elements, this finite element model will achieve the best precision. However, this model has to involve too much computational task to be accecpted by current computer capability. Therefore, each pipe in the structure is always discreted by one beam element, and the joints are igored. Model test and numerical analysis shows this kind of finte element model always overestimate the ductility and loading capacity of the structrure. Therefore, refined finite element method for grid structure is studied in this paper, this method can achieve the same precision as the model using solid element, and reduce the computational task greatly, by selecting the type, size, and zone discrretized automatically.If the load on the grid structure is small, the pipes in the structure can be discreted by beam element. To judge if the length and shape functions of a beam element are suitable, firstly the deflection function is derived when the beam are tensiled,pressed, and purely bended according to the boundary conditions from finite element trial analysis, and then the generalised force field are obtained. Secondly, based on the Zienkiewicz-Zhu error post-processing technique, this generalised force field can be used as a relativly accurate solution, the energy norm of the finite element solution and the relatively accurate solution is given to decide the raltive error of the beam element. The computation trials proceeds after the shape function and the length of beam element is adjusted, until the relative error of every beam element in the structure is satisfied.Before the joint has plastic strain, its rigidity can be measured. To consider the volume and rigidity of the joint, a rigid panel element with the same length as the radius of the welded hollow spherical joint is set to simulate the volume of the joint, and a spring element is set between the rigid panel and the pipe to simulate the rigidity of the joint. The element matrix of the beam considering both the rigid panel and the joint rigidity is given. With the empirical stiffness equation of hollow sphere joint, the influencing range of the joint to the axial stiffness and the rotation stiffness are calculated. The energy norm is used to analyze the axial rigidness and the rotation rigidness error to the displacement solution.The joints and the pipes will yield or collapse as the load increases, and the finite element model with only beam element can not simulate this phenomenon. Multi-scale finite element model is employed to solve this problem.To consider the bending collapse of the pipes in the reticulated frames, based on the multi-scale simulation, the part of member that having bending collapse is divided by the shell elements or solid element as a micro-model, and the other part of the member was simulated by beam elements as a macro-model. The method to couple the beam elements and the shell element is given. The location of the micro-model is predicted by the stress field of the beam element, after the beam element is adjusted by adptive finite element method. The length of the micro model is adjusted by the plastic work increment in the microl model.To analyze the structure after the joints yielded, based on the multi-scale simulation, the joint and a shot part of each member connecting to it is divided by the solid element as a micro-model, and the other part of structure is simulated by beam elements as a macro-model. The incremental displacement constraint equations for the nodes on the section between the two models are derived based on the plane section premise of classical beam theory. A method to couple the beam element and the solid element is given. The pipe length connecting to the joint is estimated and the Zienkiewicz-Zhu error post-processing technique is used to check its validity.Theroy analysis and numerical test show that the refined finite element method can achieve almost the same accuracy with the finite element model using only solid element, while reduce computianal task greatly. Finally, the conclusions and the problems of refined finite element method that can be studied further are summarized about reifined finite element method at the end of this thesis.