| With the development of modern bridge structure aiming for long span, complicated structure and light type, the need to improve calculation accuracy and efficiency of spatial nonlinearity analysis for bridge structure is urgent. On the basis of researching the related literature home and abroad, the following work has been done as:1, Based on co-rotational procedure and static balance condition, a geometrical non-linear tangent stiffness matrix of plane truss element in global coordinate system has been successfully derived by means of differential method, and total algorithm of nodal force has also been acquired. The numerical results demonstrate that these formulations are simple but highly accurate.2, The co-rotational formulations of plane beam element for geometrical nonlinear in existing literatures has been improved because that geometric parameters of instant configuration rather than initial configuration is adopted to calculate displacement and strain in this paper. Moreover, according to the mechanical characteristics of hinged beam that bending moment is equal to zero and the characteristics of no deformation but rigid motion of the forced rigid arm, the explicit expressions of nonlinear tangent stiffness matrix of plane beam element with rigid arms or hinges in both ends are obtained by employing differential method. The Numerical results demonstrate that the proposed plane beam element can solve the structural analysis of plane beam with rigid link or hinge. Moreover, the developed beam element is valid and practicable due to the same format as the general beam element without rigid arms or hinge.3, The above-mentioned has been extended from only geometrical nonlinearity to geometrical and material bi-nonlinearity algorithm by taking a prestressed concrete as an example. A numerical model for a given section considering material and geometrical nonlinear analysis of prestressed concrete beam element is developed. Firstly, by means of virtual work, a tangent stiffness matrix for material nonlinearity of perfectly-bonded prestressed concrete beam element is derived in co-rotational coordinate system. Then, through building total and incremental relationships derived from differential equations of nodal displacements and forces between global coordinate system and co-rotational coordinate system, respectively, tangent stiffness in global coordinate system prestressed concrete beam element is developed considering geometric and material nonlinearity. Nonlinear analysis of several reinforced concrete and prestressed concrete structure have been performed to demonstrate the usefulness of the developed method.4, Based on co-rotational procedure, the geometrical and material bi-nonlinearity tangent stiffness matrix of spatial truss element in global coordinate system has been developed because that this element can simulate prestressing steels. Combined with the existing nonlinear degenerated shell element, the tangent stiffness matrix of nonlinear composite elements has been derived by use of internal displacement field model of degenerated shell element. The nonlinear analysis of several reinforced concrete and prestressed concrete structures have been employed to verify the effectiveness of the developed method.5, Taking quadrilateral8-node plane element as an example, geometrical nonlinear element tangent stiffness matrix for plane stress element under a large rotation with small strain is presented based on co-rotational procedure. The above-mentioned algorithm has been extended from only geometrical nonlinearity to geometrical and material bi-nonlinearity when shear stress τ13and τ23of principal plane are0in layered model of degenerated shell element mentioned in the third chapter, it is special for plane stress element, Thus the constitutive relation yield criterion and failure criteria of concrete for degenerated shell element can been used for bi-nonlinearity plane stress element, Firstly, by means of virtual work, a tangent stiffness matrix for material nonlinearity of perfectly-bonded reinforced concrete beam element is derived in co-rotational coordinate system. Then, through building total and incremental relationships derived from differential equations of nodal displacements and forces between global coordinate system and co-rotational coordinate system, respectively, tangent stiffness in global coordinate system reinforced concrete beam element is developed considering geometric and material nonlinearity. Nonlinear analysis of several reinforced concrete and prestressed concrete structure have been performed.6, In order to improve calculation accuracy and efficiency of spatial nonlinearity analysis for concrete filled steel tube arch. In this paper, based on co-rotational procedure, a numerical model considering material and geometrical nonlinear analysis for concrete filled steel tube beam element is developed. Firstly, using Euler formulas and variable method, a tangent stiffness matrix for material nonlinearity of perfectly-bonded concrete filled steel tube beam element is derived in co-rotational coordinate system by means of virtual work. Then, based the method as nonlinear analysis of plane beam element, the method has been extended from geometric nonlinearity to Bi-nonlinearity, that is to say, the small strain is assumed as linear strain-stress relation in co-rotational coordinate system. The tangent stiffness for material nonlinearity in co-rotational coordinate system is developed based on method mentioned in chapter two. Thus, a tangent stiffness in global coordinate system concrete filled steel tube beam element is developed considering geometric and material nonlinearity. Plane and spatial comparisons between the results in this paper and those from model test of concrete-filled steel tubular arch rib shows the accuracy of the developed method is very high.7, In order to analyze the coupled effect of geometric nonlinearity and concrete creep for long-span concrete structures, based on Euler-Rodrigues formula for spatial rotation, a tangent stiffness matrix of spatial beam considering geometric nonlinearity using the method mentioned in Chapter6in co-rotational coordinate. Compared with method in Chapter6, the developed method in this chapter can separate the displacement and deformation of rigid body, and then decrease calculation error when the deformation is large. Using the method of plane beam considering hinge and rigid arm of beam end, based on the mechanical characteristics of hinged beam that bending moment is equal to zero and taking rigid arm as spatial vector, the explicit expressions of nonlinear tangent stiffness matrix of plane beam element with rigid arms or hinges in both ends are obtained by employing limit rotation formulas of spatial vector differential method. Based on this, refer to the algorithm of concrete shrinkage and creep, the explicit expressions of spatial beam element considering concrete shrinkage and creep is developed in co-rotational coordinate system. Finally, a geometric nonlinearity analysis of concrete tower of hybrid beam cable-stayed bridge has been performed considering concrete shrinkage and creep. |
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