A consistent 3D corotational beam element for nonlinear dynamic analysis of flexible structures

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.

Safety assessment of structures for near-field blast-induced ground excitations using operational modal analysis

This paper presents a nonlinear modeling method for dynamic analysis of flexible structures undergoing overall motions that employs the mode approximation method. This method, different from the naive nonlinear method that approximates only Cartesian deformation variables, approximates not only deformation variables but also strain variables. Geometric constraint relations between the strain variables and the deformation variables are introduced and incorporated into the formulation. Two numerical examples are solved and the reliability and the accuracy of the proposed formulation are examined through the numerical study.

The new trend toward modern earthquake-resistant design of buildings based on nonlinear dynamic analysis accounting for peak and energy demands requires efficient ground motion record selection procedures. For this reason, in the present work, two record selection strategies based on acceleration and input energy spectrum considering the spectral shape via Np are presented. Furthermore, both record selection strategies are optimized by means of four artificial intelligence (AI) techniques: Genetic Algorithms (GA), Harmony Search (HS), Particle Swarm Optimization (PSO) and Vibrating Particle System (VPS). In particular, the effectiveness of each AI approach toward the best set of ground motion records for nonlinear dynamic analysis is compared. For this aim, spectral acceleration and input energy design spectra were considered, as well as 1024 seismic records obtained from the Pacific Earthquake Engineering Research Center. For all the AI or meta-heuristic approaches, the fitness function used is focused on minimizing the difference between the average spectrum of eleven ground motion records and the design spectrum using the well-known parameter Np, which represents the spectral shape in a range of periods. In addition, a penalization is included for those spectra with very large or low demands. Thus, 24 sets of eleven seismic records that can be used for nonlinear dynamic analysis of structures with a fundamental period of vibration of 0.6, 1.2 and 1.8 seconds were obtained and purposes. The results demonstrate the ability of the two records selection strategies analyzed and the four meta-heuristic procedures, achieving results quickly and simply regardless of the type of demands, intensities and periods considered. Finally, it is concluded that the VPS algorithm is better in comparison with GA, HS, and PSO since it obtains superior results in almost all the selected cases.

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.

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.

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.

To obtain an accurate insight into the behavior of most realistic steel frames, joint flexibility should be allowed for in the analysis. So far, most research work is concentrated on the linear and nonlinear static analysis of steel frames with flexible connections. Very few papers were contributed to the dynamic and vibration analysis of these types of frames. This paper proposes a numerical method for linear and nonlinear vibration analysis of frames with semirigid connections. The special features about this method are the derivation and the use of a shape function with end springs to formulate the element matrices. The effects of initial stress and of the change of joint stiffness due to the applied load are accounted for in the suggested method, which is believed to be more general than the existing methods for vibration analysis of flexibly connected steel frames.

In this work, a new method for nonlinear time-history earthquake analysis of 2D steel frames by a fiber plastic hinge method is presented. The beam-column element based on the displacement-based finite element method is established and formulated in detail using a fiber plastic hinge approach and stability functions. Geometric nonlinearities are taken into accounting by stability functions and the geometric stiffness matrix. A nonlinear dynamic algorithm is established based on the combination of the Newmark integration method and the Newton-Raphson iterative algorithm for solving dynamic equations. The proposed program predicts the nonlinear inelastic responses of 2D steel frames subjected to earthquakes as efficiently and accurately as commercial software. This study also shows that the initial residual stresses of steel should be considered in nonlinear inelastic time-history earthquake analysis of 2D steel frames while SAP2000 does not consider the effects of residual stresses.

In this study, the nonlinear analysis and seismic appraisal of composite frames having concrete filled steel tube columns (CFSTs) were investigated. The case study composite frames were made of the square columns surrounded by steel tube outside and infilled with concrete, and also steel I beams. These frames were taken as 4, 6 and 8 stories with three equal bays. Then, the nonlinear pushover analysis was applied to examine the influence of variation in the width-thickness ratio, slenderness ratio, yield strength of the steel tube and compressive strength of the concrete within the columns of each frame. Thus, a total of seventy-two different composite frame models with CFST columns and steel beams were examined in accordance with the response parameter of the base shear-top displacement. The obtained results were discussed comparatively as per the lateral capacity and initial stiffness. It was observed that the material and dimensional properties of the CFST columns influenced significantly the seismic behavior of the composite frames.

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 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.

A review on computational linear and nonlinear dynamic analysis of shell-type composite 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.