Research And Program Design Of Nonlinear Beam,plate And Shell Element Based On Co-rotation Method

The long-span,high-rise and light-weight development trend of bridge engineering puts forward efficient and accurate calculation requirements for the development of structural finite element analysis theory and calculation methods.The element coupling in the engineering structure system is more complex,which makes the nonlinear effect of the long-span structure more obvious under the condition of large displacement and large rotation.in the analysis of large deflection and nonlinear buckling of traditional thin-walled structures,there are some phenomena,such as membrane locking,element singularity,uncoordinated coupling deformation and so on.Solving the problem of finite element analysis accuracy of this kind of engineering structure can not only reduce the engineering cost and avoid blind test,but also better understand the mechanical behavior and stress law of the structure,and provide experience for safer and more efficient structural design.The finite element nonlinear numerical algorithm based on the co-rotating formula uses the rotating coordinate system to separate the rigid body displacement from the pure deformation displacement.at the same time,the material nonlinear effect can be calculated independently in the rotating coordinate system,which has the characteristics of simpler and more efficient solution.Based on the co-rotation formula,this paper extends the analysis of linear element to the analysis of large displacement,large rotation and small deformation response,and uses self-programming software to develop an element calculation program considering material nonlinearity and geometric nonlinearity under large deflection and linear buckling effect.the main contents are as follows:(1)The relationship between section force and rod end deformation of nonlinear fiber beam-column element under multi-axial loading based on flexibility method is derived.The nonlinear analysis flow of the flexibility method is given,and the corresponding program is compiled to prove that the material nonlinear calculation based on the flexibility method element is almost not disturbed by the geometric nonlinear behavior.For long-span bridges,there is no need to divide too many elements to meet the calculation accuracy.(2)The quaternion matrix is used to make up for the disadvantage of non-superposition of the corner of the spatial element,provides a way to store and update the corner in the process of nonlinear iteration,and deduces the co-rotation formulation which is independent of the specific formulation of the element.so that the units with different attributes can be written uniformly,which is more suitable for program development.(3)The geometrically nonlinear co-rotational formulas of spatial beam element and shell element with shear resistance are derived respectively.Both of them have good accuracy and efficiency in the analysis of large deflection and nonlinear buckling effect.(4)The secondary development of the spatial beam element considering geometric nonlinearity is carried out by using the UPFs user programmable characteristic of ANSYS,which makes up for the lack of analysis ability of self-programming software.the static analysis of the bridge is carried out,and compared with the calculation results of beam188 element,the errors of axial force,shear force and bending moment are kept at about 2%,which proves the practicability and accuracy of the element.