Extremely large displacement dynamic analysis of elastic–plastic plane frames

Abstract

This paper presents a numerical analysis of large displacement responses of elastic-plastic plane frames under static and dynamic loads, by applying the vector-form intrinsic finite element method. The VFIFE method defines the structure into a number of mass points, and applies Newton's second law and the internal force equilibrium to describe the motions of each mass point. By tracing the motions of all the mass points, it can analyze the large geometrical and material nonlinear changes during the motion of the structure without using the geometrical stiffness matrix and iterative procedures. Three different numerical examples are presented to demonstrate both the capability and the accuracy of the VFIFE method in a nonlinear dynamic analysis of frame structures with extremely large displacement.CR formulation based on a convected material frame. All of these methods are rather effective for analyzing the transient responses of structures made of inelastic materials and large deformation characteristics [9]. For nonlinear material structures, most of the existing nonlinear material models can be classified into two main categories: lumped and distributed plasticity models. The lumped model is an efficient way to represent inelasticity in frames. A typical finite element method (FEM) considering the geometrical and material nonlinearities requires iterations at each incremental step to achieve the equilibrium [10]. This method encourages flexural yielding and can ensure that plastic hinge rotation will occur at the member ends rather than along the column length. The second-order plastic hinge concept based on the use of stability interpolation functions has been proposed for frame structure analysis [11][12][13][14][15][16][17]. Marante et al. [18] proposed a general criterion of localization and two plastic hinges at the end of the frame member. Some researches improved the lumped plastic hinge method, such as for example the distributed plasticity model (also called plastic-zone model), which allows for the gradual spread of yielding within the member. In the distributed plasticity model, the frame element stiffness can be computed by using either the displacement [19] or the force-based approach [20][21][22]. This allows plastic hinges to form at any location in an element. In addition, the element cross-section can be a fiber section using different stressstrain models for different fibers within the cross-section. Without properly taking into account the internal forces due to pure deformations, most of these studies may not be able to simulate inelastic structural responses of moving structures subjected to extremely large displacements or deformations.Another type of method, the discrete numerical method is suitable to study large deformation, cracking and failure of structures. For example, the rigid-body spring model (RBSM) was proposed by Kawai and Kondou [23]. In this model, each element consists of rigid bodies with two springs, called normal and shear springs which allow the restoring forces to be ...

Real-time hybrid simulation based on vector form intrinsic finite element and field programmable gate array

“…Unconditional stable numerical schemes may be employed in the future study. The numerical substructures used in this proposed RTHS platform are all linear structural system with small deformations. More refined and complicated structural behaviors such as the elastoplastic model, and the hysteretic model shall be considered in the numerical substructure for the VFIFE‐based RTHS.…”

“…The unit vector, e n + 1 , in the convected coordinate of the element is updated as As the predicted values of x n + 1 and β n + 1 are absolute displacements, rigid‐body motions need to be tilted out to obtain pure deformation. Virtual reverse motion is adopted herein to eliminate rigid body motion, and a reference node, such as a in Figure , is selected. Rigid‐body translation d , between and , can then be tilted out as in Figure b.…”

“…In this paper, a parallel RTHS platform is proposed based on the vector form intrinsic finite element (VFIFE) and the field programmable gate array (FPGA), which can effectively relieve the computational burden in RTHS with a numerical model containing many DOFs. The VFIFE is a method of structural analysis developed by Ting et al to handle nonlinear dynamic problems involving large deformations or rigid motions . Many studies on structural nonlinearity have been carried out using the VFIFE.…”

“…Lien et al simulated the nonlinear behavior of steel structures on fire . Wang et al carried out the large‐displacement dynamic analysis of elastic–plastic frame beams . Duan et al analyzed the entire process of the collapse of a mock‐up cable‐stayed bridge in an earthquake .…”

Form-control of shell structures generated from hanging models with target heights

“…Proposed by Ting et al 14,15 and Shih et al, 16 it is a relatively new and promising numerical analysis method. Since its proposal, many scholars [20][21][22][23][24] have done research using the VFIFE method for complicated behavior analysis of structures, including geometric nonlinearity, material nonlinearity, mechanism motion, dynamic responses, and buckling or wrinkles failure. Li et al 25 have successfully applied the VFIFE method to determine structurally efficient forms of shell structures generated from three types of physical models, which are the hanging models, the tent models, and the pneumatic models.…”