Complementarity Framework for Nonlinear Analysis of Tensegrity Structures with Slack Cables

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.

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

Nonlinear structural analysis, which can account for geometrical or material nonlinearities beyond the scope of linear methods, typically incurs high computational costs. Recent advances have shown that quantum computers can accelerate various numerical simulations. Although quantum acceleration of linear structural analysis via the Quantum Linear System Algorithm (QLSA) has been studied, its application to nonlinear structural analysis remains unexplored. Here, we introduce our proposed quantum algorithm for accelerating nonlinear structural analysis, summarizing its key features and performance results from our recent study.

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.

The dynamic response of nonlinear structures has been a topic of interest in civil engineering research. Problems in which base-structure interaction is present have a great importance in structural analysis, since most structures rests on flexibel systems (soil or supports with dissipation). In this research area, the study of structures under the action of seismic loads represent a relevant topic, since this kind of excitations may excite several vibration modes and thus influence strongly the dynamic response. In this context, the prediction of the nonlinear structural behavior in frequency domain of structures under base excitation is a useful resource to assess the potential effects of sismic loads on these systems. In this thesis, a methodology for nonlinear dynamic analysis of plane frame structures under base excitation is presented considering geometric nonlinearity and elastic supports represented by elasto-plastic unidimensional springs. Trough a parametric analysis, the variability of the dynamic responses of slender structural systems under the actions of real earthquakes, synthetics earthquakes, as well as the action of multiple earthquakes is assessed. The structural systems here analyzed are discretized in space using a nonlinear finite element formulation. For the response in frequency domain, a scheme based on the Balance Harmonic Method and the Galerkin method, in conjunction with continuation methods, is formulated to obtain the nonlinear resonance curves. The nonlinear dynamic response in the time domain is calculated by direct integration of the equations of motion. For this, the Runge-Kutta method and the Newmark method in association with the iterative Newton-Raphson scheme are employed.

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.

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.

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.

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

Given the vast advancements in computing power in the last several decades, nonlinear dynamic analysis has gained wide acceptance by practicing engineers as a useful way of assessing and improving the seismic performance of structures. Nonlinear structural analysis software packages give engineers the ability to directly model nonlinear component behavior in detail, resulting in improved understanding of how a building will respond under strong earthquake shaking. One key component, in particular, for understanding the behavior of moment-resisting frames is the plastic rotation of the flexural hinges. Performance-based standards typically use plastic rotation as the primary parameter for defining the acceptance criteria in moment-resisting frames. Since plastic rotation is a key parameter in the seismic damage assessment, the concept as well as the method to calculate this quantity must be understood completely. Though engineers rely on the plastic rotation output from seismic structural analysis software packages to determine acceptable performance, the actual calculation methods used in achieving such plastic rotation quantities usually lay within a so-called “black box”. Based on the outputs obtained from most structural analysis software packages, it can be shown that running an algorithm considering material nonlinearity by itself will produce reasonably accurate results. Moreover, separately running an algorithm considering geometric nonlinearity also can produce accurate results. However, when material nonlinearity is combined with geometric nonlinearity in an analysis, obtaining accurate results or even stable solutions is more difficult. The coupling effect between the two nonlinearities can significantly affect the global response and the local plastic rotation obtained from the analysis and therefore needs to be verified through some analytical means. Yet, the verification process is difficult because a robust analytical framework for calculating plastic rotation is currently unavailable and urgently needed. In view of this gap, an improved analytical approach based on small displacement theory is derived to calculate the plastic rotations of plastic hinges at various locations of moment-resisting frames. Both static and dynamic analysis with nonlinear geometric effects will be incorporated in the derivation. Here the element stiffness matrices are first rigorously derived using a member with plastic hinges in compression, and therefore the coupling of geometric and material nonlinearity effects is included from the beginning of the derivation. Additionally, plastic rotation is handled explicitly by considering this rotation as an additional nonlinear degree-of-freedom. Numerical simulation is performed to calculate the nonlinear static and dynamic responses of simple benchmark models subjected to seismic excitations. Results are compared with various software packages to demonstrate the feasibility of the proposed method in light of the output results among software packages in calculating plastic rotations.

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.

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

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.