Papers by Keyword: Geometric Nonlinear

Abstract: In this paper, some numerical verifications would be presented and discussed, mainly including the following three types: (1) the pure bending beam in which the structural stiffness would maintain the original value and not change along with the load; (2) the clamped arc-beam in which the structural stiffness would decrease gradually with the increment of load and the structure would be buckling at some certain load value; and (3) the cantilever beam in which the structural stiffness would increase significantly with the increment of load. For all of the above examples, the present results are in good agreement with the analytical results and numerical results in other literatures, testifying and illustrating the validity of the large rotation matrix for nonlinear framed structure, which is developed in the part 1 of this paper.

Abstract: In this paper, a large rotation matrix for geometric nonlinear analysis of frame structures is developed by introducing the Rodrigues formula proposed by Argyris to modify the original rotation scheme of Bathe and Bolourchi. In the deduction, the large rigid body rotation of the beam element is decomposed into the relative translational displacements and the axial rotation respectively. Using Rodrigues formula, the large rotation matrix of rigid body can be calculated and sequentially the nodal transformation matrix of the beam element can be derived. And with this transformation matrix, the equilibrium equations of the beam elements established in the current configuration can be transformed into the original configuration, and then assembled and solved finally. The validity verification of the method would be presented and discussed in the part 2 of this paper.

Abstract: Based on a co-rational (CR) framework, a 2-noded element formulation of 3D truss was presented, which was used for accurately modeling of suspension bridges with large displacements and rotations. The CR framework could consider the out-plane stiffness by the geometric stiffness, which was applicable to the analysis of 3D cable bridges. Using the co-rational truss united with the energy convergence criteria and the Newton with Line Search Algorithm, the nonlinear behavior of 3D cable structural system was simulated conveniently and accurately. Therefore, the traditional truss elements based on elastic modulus modified method and complex catenary elements were avoided. In order to simulate the hanging of girder and the structural system changing during the construction, the elements’ killing and activating methods were realized by the modulus modified methods.

Abstract: Based on the geometric deformation of the Euler-Bernoulli beam element, the geometric nonlinear Euler-Bernoulli beam element based on U.L. formulation is derived. The element’s transverse first-order displacement field is constructed using the cubic Hermite interpolation polynomial, and the first-order Lagrange interpolation polynomial is used for the axial displacement field. Then the additional displacements induced from the rotation of the elemental are included into the transverse and longitudinal displacement fields, so those displacement fields are expressed as the quadratic function of nodal displacement. Afterwards the nonlinear finite element formulas of Euler-Bernoulli beam element under the form of U.L. formulation are derived using Cauchy strain tensor and the principle of virtual displacements. The total equilibrium equation and tangent stiffness for large displacement geometric nonlinear analysis of frame are obtained in the total coordinate system. The correctness of this element is proved by typical example.

Abstract: The geometric nonlinear dimensionless dynamical equations of suspension spring cushioning packaging system were established and a new concept of damage boundary curves of the system was developed under the action of rectangular pulse. Considering the angle of the suspension spring ,a three-dimension damage boundary curve is obtained.The mathematic results of the equation are calculated by using the four steps Runge-Kutta method. Studies have shown that the dimensionless pulse peak, the angle of suspension spring and the damping ratio of the system can affect the safe region, and that increasing damping can enlarge the safe region of the system. The shock of the packed product can reduce by adjusting the parameters of the system properly. These results have important application value in design of the suspension cushioning system.

Abstract: Based on the stability theory, one roof structure with steel tubular arch-truss was taken as a research object. Linear buckling, geometric nonlinear stability and elastic-plastic nonlinear stability were investigated by applying ANSYS finite element software, and the relational curves of critical load-displacement were obtained. The analysis results show that material nonlinear makes obvious influence on the stability of the structure, material nonlinear and geometric nonlinear are taken into account at the same time can make a better understanding of the structural stability performance.