A three-dimensional beam element is derived based on the principle of stationary total potential energy for geometrically nonlinear analysis of space frames. A new tangent stiffness matrix, which allows for high order...A three-dimensional beam element is derived based on the principle of stationary total potential energy for geometrically nonlinear analysis of space frames. A new tangent stiffness matrix, which allows for high order effects of element deformations, replaces the conventional incremental secant stiffness matrix. Two deformation stiffness matrices due to the variation of axial force and bending moments are included in the tangent stiffness. They are functions of element deformations and incorporate the coupling among axial, lateral and torsional deformations. A correction matrix is added to the tangent stiffness matrix to make displacement derivatives equivalent to the commutative rotational degrees of freedom. Numerical examples show that the proposed dement is accurate and efficient in predicting the nonlinear behavior, such as axial-torsional and flexural-torsional buckling, of space frames even when fewer elements are used to model a member.展开更多
The second order effect is the interaction between the vertical load and the deformation in a vertically forced element. In order to deduce a more brief but practical method, which has considered the second order effe...The second order effect is the interaction between the vertical load and the deformation in a vertically forced element. In order to deduce a more brief but practical method, which has considered the second order effect in a sway frame, some factors which affect the second order deformation in a sway frame should be generalized based on a more accurate method. Nonlinear finite element is adopted in this paper, and according to this theory, a program, which can calculate the inner force and the deformation of the sway frame considering the second order effects is coded.展开更多
文摘A three-dimensional beam element is derived based on the principle of stationary total potential energy for geometrically nonlinear analysis of space frames. A new tangent stiffness matrix, which allows for high order effects of element deformations, replaces the conventional incremental secant stiffness matrix. Two deformation stiffness matrices due to the variation of axial force and bending moments are included in the tangent stiffness. They are functions of element deformations and incorporate the coupling among axial, lateral and torsional deformations. A correction matrix is added to the tangent stiffness matrix to make displacement derivatives equivalent to the commutative rotational degrees of freedom. Numerical examples show that the proposed dement is accurate and efficient in predicting the nonlinear behavior, such as axial-torsional and flexural-torsional buckling, of space frames even when fewer elements are used to model a member.
文摘The second order effect is the interaction between the vertical load and the deformation in a vertically forced element. In order to deduce a more brief but practical method, which has considered the second order effect in a sway frame, some factors which affect the second order deformation in a sway frame should be generalized based on a more accurate method. Nonlinear finite element is adopted in this paper, and according to this theory, a program, which can calculate the inner force and the deformation of the sway frame considering the second order effects is coded.
