| The non-linear finite element analysis method is an important research method for the analysis of the mechanical performance of large-span and space structures.In practical engineering,concrete members are often under the common stress state of axial force,shear force and bending moment,and are the main load-bearing members and anti-side force members.In addition,serving in a corrosive environment is often the normal working state of many structural components,especially in recent years,environmental problems have become the focus of attention,and structural damage caused by corrosion is an important reason that affects structural stability and durability.Therefore,studying the working mechanism of corroded concrete-filled steel tube members under the complex stress state of compression,bending and shear has important scientific research value and practical engineering reference significance for accurately assessing the safety of concrete-filled steel tube structures.In this paper,the iterative solution of the nonlinear static equations is derived and deduced,and the the fiber beam element model considering the shear effect is mainly derived.Combining the elastic-plastic mechanics incremental theory with the fiber beam element model,and then establishes the nonlinear finite element analysis theory of structure under complex stress condition.Based on this theory,the MATLAB calculation and analysis program is compiled,and the calculation example analysis and numerical simulation verification are carried out.Finally,the previous research results in this article are applied to the nonlinear finite element analysis of the horizontal bearing capacity of corroded concrete-filled steel tube under compression,bending and shear.The relevant parameters affecting the horizontal bearing capacity of this type of member are analyzed,and the calculation of the horizontal bearing capacity coefficient is obtained.The research content is as follows:Firstly,research on the iterative solution method of nonlinear static equations in the whole process of structural nonlinear analysis.A new method of displacement control is deduced and sorted out,and the corresponding analysis program is compiled using MATLAB software,which is verified by a combination of typical geometric nonlinear calculation examples and material nonlinear calculation examples.The results show the accuracy and feasibility of the new displacement control method.Secondly,the fiber beam element model that can consider the shear effect is derived and deduced.Based on the Timoshenko beam theory,the displacement mode is determined by defining the force and deformation of the three-dimensional fiber beam element in space,and the interpolation function matrix is obtained.Based on the continuum medium mechanics and the principle of virtual displacement,the elastic stiffness matrix and geometric stiffness matrix of the model are deduced and the tangent stiffness matrix for spatial nonlinear analysis is obtained.The coordinate transformation matrix is obtained based on the modified Lagrangian（U.L.）formulation.Thirdly,based on the incremental theory of elastic-plastic mechanics,combined with the relevant research conducted in the previous stage of this article,a complete set of nonlinear finite element analysis theory of structures under complex stress states that can consider both the geometric non-linearity of the structure and the non-linearity of the material is formed.Corresponding analysis programs are compiled using MATLAB software to perform nonlinear finite element analysis on typical examples of reinforced concrete and concrete-filled steel tube under compression,bending and shearing,which verifies the correctness of the method used in this paper.Fourthly,according to the non-linear finite element analysis theory of structure under the complex stress state of compression,bending and shear established in this paper,the mechanical properties of concrete filled steel tube columns after corrosion are analyzed,and the accuracy of the model established in this paper is verified by numerical simulation of related experiments in the existing literature.Then,the relevant research on the horizontal bearing capacity of the local corrosion of concrete-filled steel tube compression,bending and shear members was carried out,focusing on the axial compression ratio,concrete strength,steel strength,steel content,corrosion rate,and slenderness ratio that may affect the force of the member.Lastly,using multiple non-linear regression analysis,the expression of the horizontal bearing capacity coefficient of the concrete-filled steel tube compression-bending-shear member after local corrosion was obtained,and the fitted value was compared with the actual value to verify the accuracy of the obtained expression. |
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