Nonlinear modeling and dynamic analysis of flexible structures undergoing overall motions employing mode approximation method

A consistent co-rotational formulation and numerical procedure for the dynamic analysis of planar Timoshenko beam is presented in detail to demonstrate the finite element analysis techniques of co-rotational formulation for nonlinear dynamic analysis of beam structures. The inertia nodal forces and deformation nodal forces are systematically derived by consistent linearization of the fully geometrically nonlinear beam theory by using the d’Alembert principle and the virtual work principle. The nodal coordinates, incremental displacements and rotations, velocities, accelerations and the equations of motion of the system are defined in terms of a fixed global coordinate system, while the total strains in the beam element are measured in element coordinates which are constructed at the current configuration of the beam element. A practical numerical procedure is proposed to determine the current end cross-section coordinates, element coordinates, and element deformations corresponding to an incremental displacement. An incremental-iterative method based on the Newmark direct integration method and the Newton-Raphson method is employed here for the solution of the 284nonlinear dynamic equilibrium equations. Numerical examples are presented to demonstrate the effectiveness of the proposed method and investigate the effect of the shear deformafion on the dynamic response of the beam structures.

Numerical model for the non-linear dynamic analysis of multi-storey structures with semi-rigid joints with specific reference to the Algerian code

The goal of this paper is to propose a nonlinear dynamic model based on experimental data and NBR-6123-87 to accomplish a nonlinear dynamic analysis of slender structures subjected to wind loading. At first we compute the static answer given by the mean wind speed. In this part of the problem we consider the concept of effective stiffness to represent the physical nonlinearity of material and aP-Delta method to represent the geometrical nonlinearity. Considering the final stiffness obtained in thatP-Delta method, we compute the dynamic answer given by the floating wind speed, according to the discrete dynamic model given by NBR-6123-87. A 40 m RC telecommunication tower was analyzed, and the results obtained were compared with those given by linear static and dynamic models.

Elastomeric bearings are commonly used in base-isolation systems to protect the structures from earthquake damages. Their design is usually developed by using nonlinear models where only the effects of shear and compressive loads are considered, but uncertainties still remain about consequences of the tensile loads produced by severe earthquakes like the near-fault ones. The present work aims to highlight the relapses of tension on the response of bearings and superstructure. To this end, three-, seven- and ten-storey r.c. framed buildings are designed in line with the current Italian seismic code, with a base-isolation system constituted of High-Damping-Rubber Bearings (HDRBs) designed for three values of the ratio between the vertical and horizontal stiffnesses. Experimental and analytical results available in literature are used to propose a unified nonlinear model of the HDRBs, including cavitation and post-cavitation of the elastomer. Nonlinear incremental dynamic analyses of the test structures are carried out using a homemade computer code, where other models of HDRBs considering only some nonlinear phenomena are implemented. Near-fault earthquakes with comparable horizontal and vertical components, prevailing horizontal component and prevailing vertical component are considered as seismic input. Numerical results highlight that a precautionary estimation of response parameters of the HDRBs is attained referring to the proposed model, while its effects on the nonlinear response of the superstructure are less conservative.

This paper discusses implementation and adaptivity of the Discontinuous Galerkin (DG) finite element method as applied to linear and non-linear structural dynamic problems. By the DG method, both displacements and velocities are approximated as piecewise bilinear functions in space and time and may be discontinuous at the discrete time levels. Both implicit and explicit iterative algorithms for solving the resulted system of coupled equations are derived. They are third-order accurate and, while the implicit procedure is unconditionally stable, the explicit one is conditionally stable. An h-adaptive procedure based on the Zienkiewicz–Zhu error estimate using the SPR technique is applied. Numerical examples are presented to show the suitability of the DG method for both linear and non-linear structural dynamic analysis. Copyright © 1999 John Wiley & Sons, Ltd.

A distributed inelasticity cyclic model of reinforced concrete (RC) columns is developed, using as a building block the tangent flexibility matrix of a section, which relates the three nondimensional normal stress resultants to the three corresponding section deformations. It is given in a companion paper in terms of the amount and distribution of the column longitudinal and transverse reinforcement. The tangent flexibility matrix of the cross section is integrated numerically along the element length to give the tangent flexibility (and stiffness, by inversion) matrix of slender reinforced concrete columns, in which flexure dominates the cyclic inelastic behavior. The model is implemented into a finite element program for the nonlinear static or dynamic analysis of structures in three dimensions. The program is applied to predict the results of cyclic uniaxial or biaxial tests, as well as the dynamic response of an actual reinforced concrete building to the three components of the Kalamata 1986 earthquake. The model predictions are in good agreement with the test results and with the damage inflicted to the building by the earthquake.

Piezoelectric composite laminates are a powerful material system that offers vast options to improve structural behavior. Successful design of piezoelectric adaptive structures and testing of control laws call for highly accurate, reliable and numerically efficient numerical tools. This paper puts focus onto linear and geometrically nonlinear static and dynamic analysis of smart structures made of such a material system. For this purpose, highly efficient linear 3-node and 4-node finite shell elements are proposed. Both elements employ the Mindlin-Reissner kinematics. The shear locking effect is treated by the discrete shear gap (DSG) technique with the 3-node element and by the assumed natural strain (ANS) approach with the 4-node element. Geometrically nonlinear effects are considered using the co-rotational approach. Static and dynamic examples involving actuator and sensor function of piezoelectric layers are considered.

A formulation of the nonlinear FEM truss element that takes into account both the geometric nonlinearity and material nonlinearity of the structure is derived. The associated iterative algorithm for the application is described. Based on two inelastic material models (isotropic hardening and dynamic hardening), three space truss structures are subjected to static and to dynamic loads in order to illustrate the application of nonlinear FEM. The nonlinear FEM described can accurately trace the complex structural behavior of space truss structures, including snap-through, and buckling. The FEM results match well with the theoretical results.

A comprehensive complementarity framework is presented for both nonlinear static and dynamic analyses of tensegrity structures with a large number of slack cables. These analyses are characterized by cables switching between taut and slack states and hence exhibit nonsmooth behaviors. The core concept is casting the original computation in each iteration step as a linear complementary problem. To deal with the geometric nonlinearity, the governing equation is formulated based on the positional formulation finite-element method, in which the nodal positions, rather than conventional nodal displacements, are adopted as generalized coordinates. By directly linearizing the governing equation, this complementarity framework is first used to study the static analysis in the small displacement regime and then extended to the large displacement case for both the static and dynamic analyses. Multiple examples are presented to demonstrate performances of the proposed complementarity framework in both the static and dynamic cases.

This paper presents a seismic response evaluation of unbonded posttensioned precast concrete moment frames that use friction dampers at selected beam ends. The dampers utilize the displacements that occur as a result of gap opening between the beam and column members during an earthquake. The parameters investigated include the number of stories, number and strength of the dampers, and amount of posttensioning. Nonlinear static and dynamic time history analyses of prototype structures show that the dampers provide a considerable amount of energy dissipation to a frame, while the posttensioning force provides a restoring effect resulting in self-centering capability (i.e., ability of the structure to return towards its undisplaced position upon unloading). The seismic design of the structures to achieve target displacement-based performance objectives is critically evaluated based on the analysis results. Comparisons with structures that use mild steel (e.g., Grade 60) reinforcement through the beam-column joints as well as structures that use only posttensioning steel (with no friction dampers) and structures that use combinations of mild steel and posttensioning steel are also provided.

This paper is about behavior assessment of moment frames with CFT composite columns under seismic loads, knowing of their behavior, and also how to determine their behavior coefficient. For this purpose, structures with this type of composite columns in three different types with different stories (4 story, 8 story and 12 story) and with 5 span are considered. Variables are the lengths of the spans and the height of the structure. These structures analyzed using Opensees software and applying dead, live and earthquake loads by nonlinear dynamic time-history analysis and structural analysis results are presented with consideration of seven different earthquake records. Finally, the responses of maximum shear force and the maximum bending moment which were formed in the column and floors of structure by applied loads are compared and the behavior coefficient is also analyzed in this study. The results show that the value of shear force, bending moment and behavior coefficient of structure change with the deformation of the sections, for example, the shear force obtained in the model with elliptic sections is less than that of other models.

This paper investigates the influence of strain rate effect on the seismic performance of Reinforced concrete (RC) frame structures subjected to far-field and near-field ground motions. An approach for the nonlinear dynamic analysis of RC frame structures considering the strain-rate sensitivity of concrete and reinforcing steel materials is proposed and its effectiveness is validated by the experimental data of RC columns under dynamic loadings. A non-dimensional index is put forward to reveal the regularities of strain rate under different types of ground motions with various intensity levels. The influences of strain rate effect and input ground motion on the seismic performance of the exemplar RC frame are studied by comparing the seismic responses and fragilities of rate-dependent structural models with those of rate-independent ones. Numerical results indicate that the strain rates in structural members increase with the ground motion intensity and the strain rates induced by the near-field pulse-like earthquakes are higher than those by the far-field and near-field non-pulse-like earthquakes. The global response, critical member response, local damage and seismic fragility are all influenced by the strain rate effect, especially under the near-field pulse-like ground motions. Neglecting the influences of strain rate effect, variations in strain rates of different structural members and inputs of pulse-like ground motions may lead to erroneous seismic performance assessments of RC frame structures.

This paper presents a simple and efficient 2D corotational formulation for geometrically nonlinear dynamic analysis of beam structures. Newmark’s implicit time-stepping scheme with the iterative predictor-corrector algorithm is employed along with the energy-convergent criterion to determine the nonlinear dynamic equilibrium stage. The validity and efficiency of the proposed formulation are verified by simulating large deformation of a swinging rubber beam. This study confirms that the proposed formulation is highly accurate and efficient. Despite the simple numerical implementation, the proposed method is reliable in performing simulations of flexible beam structures undergoing extremely large deformation or even a chaotic motion.

Seismic evaluation of steel plate shear wall systems considering soil-structure interaction

Surrogate SDOF models for probabilistic performance assessment of multistory buildings: Methodology and application for steel special moment frames