Generalized Displacement Control Method Research Articles

Maximum-entropy meshfree method for nonlinear static analysis of planar reinforced concrete structures

A meshfree method for nonlinear analysis of two-dimensional reinforced concrete structures subjected to monotonic static loading is presented. The concrete model is implemented in the context of the smeared rotating crack approach. The stress–strain relationship for steel bars accounts for the surrounding concrete bonded to the bar (tension stiffening effect). The principle of virtual work (variational form) is used to setup the nonlinear system of equations. Maximum-entropy basis functions are used to discretize the two-dimensional domain and background cells are adopted to facilitate the numerical integration. The generalized displacement control method is implemented to solve the nonlinear system of equations and to obtain the softened structural response beyond the maximum load capacity. The proposed meshfree methodology is used to study the nonlinear behavior of reinforced concrete shear walls. Comparisons with experimental data and finite element analysis indicate that the proposed maximum-entropy meshfree method is a viable approach for nonlinear simulations of planar RC structures.

Nonlinear inelastic analysis of concrete-filled steel tubular frames

This paper presents a reliable numerical procedure for the nonlinear inelastic analysis of concrete-filled steel tubular frames. Geometric nonlinearities are taken into account by the use of stability functions derived from the exact stability solution of a beam–column subjected to axial force and bending moments. The spread of plasticity over the cross section and along the member length is captured by tracing the uniaxial stress–strain relationships of each fiber on the cross sections located at the selected integration points along the member length. The nonlinear equilibrium equations are solved using an incremental-iterative scheme based on the generalized displacement control method because of its general numerical stability and efficiency. The accuracy of the proposed procedure is verified by comparisons of the obtained results with experimental data and existing solutions. The proposed numerical procedure proves to be a reliable tool for the nonlinear analysis of concrete-filled steel tubular structures.

Second-order inelastic analysis of steel suspension bridges

The second-order inelastic analysis based on the refined plastic hinge model is proposed to predict the ultimate strength and behavior of steel suspension bridges. The cable members are modeled using the catenary cable element, while the girder and tower members are modeled using the beam-column element. The nonlinear equilibrium equations are solved using an incremental–iterative scheme based on the generalized displacement control method. This algorithm can accurately trace the equilibrium path of nonlinear problems with multiple limit points. Several numerical examples are presented. The obtained results are compared well with the existing results and those generated using the commercial finite element packages of SAP2000 and ABAQUS. It can be concluded that the proposed method is suitable for adoption in practice.

Nonlinear inelastic analysis of space frames

In this paper, a fiber beam–column element which considers both geometric and material nonlinearities is presented. The geometric nonlinearities are captured using stability functions obtained from the exact stability solution of a beam–column subjected to axial force and bending moments. The material nonlinearities are included by tracing the uniaxial stress–strain relationship of each fiber on the cross sections. The nonlinear equilibrium equations are solved using an incremental iterative scheme based on the generalized displacement control method. Using only one element per member in structure modeling, the nonlinear responses predicted by the proposed element compare well with those given by commercial finite element packages and other available results. Numerical examples are presented to verify the accuracy and efficiency of the proposed element.

Large deflection inelastic analysis of space trusses using generalized displacement control method

This paper presents the large deflection inelastic analysis of space truss structures including both geometric and material nonlinearities. The geometric nonlinearity is considered, based on an updated Lagrangian formulation, while the material nonlinearity is accounted for by tracing a complete stress–strain relationship in the elastoplastic range. The nonlinear equilibrium equations are solved using an incremental-iterative scheme based on the generalized displacement control method. This algorithm can accurately trace the equilibrium path of nonlinear problems with multiple limit points and snap-back points. A computer program is developed to predict the inelastic post-buckling behavior of space trusses. Numerical results obtained from the developed program are compared with those reported in the literature to demonstrate the accuracy of the proposed procedure.

Finite element analysis of thin-walled composite laminated beams with geometrically nonlinear behavior including warping deformation

A finite element model for structural analysis of composite laminated thin-walled beam structures, with geometrically nonlinear behavior, including torsion warping deformation, is presented. A general continuum formulation considering the updated Lagrangean procedure and a generalized displacement control method, are used to describe the deformation of the structure. The beam cross-section geometry is discretized by quadratic isoparametric finite elements to determine its bending-torsion properties. The structural discretization is performed throughout three-dimensional two-node Hermitean finite beam elements, with seven degrees-of-freedom per node. Several applications are presented, addressing the influence of lamina orientation on the structural behavior.

Practical advanced analysis software for nonlinear inelastic analysis of space steel structures

This paper presents a practical advanced analysis software which can be used for nonlinear inelastic analysis of space steel structures. The software employs the stability functions and the refined plastic hinge model to minimize modeling and computational time. The generalized displacement control method is adopted to solve the nonlinear equilibrium equations. This algorithm can accurately trace the equilibrium path of the nonlinear problem with multiple limit points and snap-back points. A user-friendly graphic interface of the software is developed to facilitate the modeling process and result interpretation of the problem. Several numerical examples are presented to verify the accuracy and computational efficiency of the proposed software by comparing the results predicted by the present software with those given by the ABAQUS and other available results.

Geometrically nonlinear static and dynamic analysis of composite laminates shells with a triangular finite element

Geometrically nonlinear static and dynamic behaviour of laminate composite shells are analyzed in this work using the Finite Element Method (FEM). Triangular elements with three nodes and six degrees of freedom per node (three displacement and three rotation components) are used. For static analysis the nonlinear equilibrium equations are solved using the Generalized Displacement Control Method (GDCM) while the dynamic solution is performed using the classical Newmark Method with an Updated Lagrangean Formulation (ULF). The system of equations is solved using the Gradient Cojugate Method (GCM) and in nonlinear cases with finite rotations and displacements an iterative-incremental scheme is employed. Numerical examples are presented and compared with results obtained by other authors with different kind of elements and different schemes.

Derivation of the higher-order stiffness matrix of a space frame element

A physical concept, the rigid body rule, is applied for the derivation of the higher-order stiffness matrix of a space frame element. The derivation has a physical meaning that is the higher-order stiffness matrix can be derived by regarding that there is a set of incremental nodal forces existing on the element, then the element undergoes a small rigid body rotation. The incremental forces should keep their magnitude and follow the rigid body motions. Then taking advantage of the established geometric stiffness matrix derived by former researchers, the higher-order stiffness matrix can be analogy derived in explicit forms without any difficulty. It can be used at the forces recovery stage in the geometric nonlinear analysis of frame structures. Meanwhile an effective numerical method, the generalized displacement control method, was adopted to trace the load–deflection curves of structures. Some famous numerical examples were tested by the element which included the proposed higher-order stiffness matrix in tangential stiffness matrix.

Nonlinear Analysis of In-Filled Steel-Concrete Composite Columns

A semianalytical method to predict the behavior of in-filled columns is presented in this paper. Moment-curvature-thrust relationships are generated for column cross sections by an iterative process. Nonlinear equilibrium equations resulting from geometric and material nonlinearities are solved by an incremental-iterative numerical scheme based on the generalized displacement control method. Square, rectangular, and circular cross sections of compact steel tubes filled with concrete are considered in the analysis. The columns are pin-ended and subjected to uniaxial or biaxial loading. The accuracy of the proposed analytical method is established by comparing the results with the corresponding experimental values.

Solution method for nonlinear problems with multiple critical points

A generalized displacement control method has been proposed for geometrically nonlinear analysis and has been proven to be bery effective by several problems with multiple limit points and snap-back points. This method can be implemented easily in a general-purpose finite-element program.