Implementation of Rayleigh Damping for Local Nonlinear Dynamic Analysis Based on a Matrix Perturbation Approach

New nonlinear FETI-DP (dual-primal finite element tearing and interconnecting) and BDDC (balancing domain decomposition by constraints) domain decomposition methods are introduced. In all these methods, in each iteration, local nonlinear problems are solved on the subdomains. The new approaches can significantly reduce communication and show a significantly improved performance, especially for problems with localized nonlinearities, compared to a standard Newton--Krylov--FETI-DP or BDDC approach. Moreover, the coarse space of the nonlinear FETI-DP methods can be used to accelerate the Newton convergence. It is also found that the new nonlinear FETI-DP and nonlinear BDDC methods are not as closely related as in the linear context. Numerical results for the p-Laplace operator are presented.

Various classical and non-classical nonlinear effects have been observed in ultrasonic wave propagation and used for contact-type damage detection. The former relates to higher harmonic generation, whereas the latter is based nonlinear vibro-acoustic modulations effects. More recently both nonlinear effects have been observed in shear horizontal wave propagation. However, the nonlinear crack-wave interaction is still not fully understood. It is assumed that this interaction is enhanced by local nonlinear elasticity and dissipation of elastic waves. The latter effect is the major focus of the paper. Previous experimental research studies demonstrate that high-frequency ultrasonic waves propagation through crack faces that are in contact–and perturbed by low-frequency excitation–exhibit local nonlinear effects of elastic and dissipative nature. The amplitude level of these effects depends on applied stresses. Both nonlinear effects have a great potential for structural damage detection. However, more theoretical and modelling research work is needed to fully understand these non-classical nonlinear effects. Numerical simulations based on nonlinear crack-wave interaction are investigated in the paper. Three models of local nonlinearity are investigated. These are: the Coulomb friction, the nonlinear viscous damping and the hysteretic stress-strain models. Nonlinear wavefield distortions–due to crack-wave interactions–are observed and analyzed. Numerical simulations are performed using the Local Interaction Simulation Approach (LISA), implemented for shear horizontal wave propagation. Wave amplitudes corresponding to generated higher harmonics and modulated sidebands are investigated in the presented work.

Complex component mode synthesis method using hybrid coordinates for generally damped systems with local nonlinearities

PurposeThe purpose of this paper is to develop robust metamodels, which allow propagating parametric uncertainties, in the presence of localized nonlinearities, with reduced cost and without significant loss of accuracy.Design/methodology/approachThe proposed metamodels combine the generalized polynomial chaos expansion (gPCE) for the uncertainty propagation and reduced order models (ROMs). Based on the computation of deterministic responses, the gPCE requires prohibitive computational time for large-size finite element models, large number of uncertain parameters and presence of nonlinearities. To overcome this issue, a first metamodel is created by combining the gPCE and a ROM based on the enrichment of the truncated Ritz basis using static residuals taking into account the stochastic and nonlinear effects. The extension to the Craig–Bampton approach leads to a second metamodel.FindingsImplementing the metamodels to approximate the time responses of a frame and a coupled micro-beams structure containing localized nonlinearities and stochastic parameters permits to significantly reduce computation cost with acceptable loss of accuracy, with respect to the reference Latin Hypercube Sampling method.Originality/valueThe proposed combination of the gPCE and the ROMs leads to a computationally efficient and accurate tool for robust design in the presence of parametric uncertainties and localized nonlinearities.

A methodology of nonlinear analysis of timber frame structures with flexible connections has been developed in this paper. The methodology is based on the results of experimental investigation of connections behavior under static and cycling loading. The adopted numerical method is based on the concept of localized nonlinearity which facilitates the reproduction of the experimentally determined connections behavior in the analysis of frame structures. The methodology is also applicable to other types of timber structures.

Optimization of sensitivity analysis in best estimate plus uncertainty and the application to large break LOCA of a three-loop pressurized water reactor

This article deals with the distributed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> -consensus estimation problem for a class of discrete time-varying random parameter systems over binary sensor networks, where the statistical information of the random parameter matrix is characterized by a generalized covariance matrix known a priori. As a binary sensor can only provide one bit of information according to a given threshold, an indicator variable is introduced so as to extract functional information (from the sensor output) that can be employed to estimate the system state. With the introduced indicator variable, a distributed estimator is constructed for each binary sensor with guaranteed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> -consensus performance constraint on the estimation error dynamics over a finite horizon. By means of a local performance analysis method, indicator-variable-dependent conditions are established for the existence of the desired distributed estimators whose gains are calculated by solving a set of recursive linear matrix inequalities. Finally, the applicability and effectiveness of the developed distributed estimation scheme are demonstrated through a numerical example.

Fish scale-like structures on substrates, arranged periodically, work together to create unique mechanical and optical behaviors. These include nonlinear stiffness, anisotropic deformation, and eventually, locking behavior. Fabrication of scale-like biomimetic examples involves embedding stiffer, plate-like sections into softer substrates. Previously, research has focused on their static qualities. The dynamic response is just as fascinating, showing remarkable interplay between geometry and materials, along with anisotropies. The damping behavior observed here significantly diverges from the conventional damping seen in mechanical frameworks, often modeled as Rayleigh damping. Here we discuss the origin of some of these behaviors that include material-geometry distinction in damping, multiple damping modes and interplay of dissipation possibilities. We have shown a derivation of simple mathematical laws estimating nonlinear spring damper system that govern architecture-dissipation relationships and can help guide design. We conclude by noting the different type of structural damping with other forms of dissipation typically encountered in mechanical behavior.

This work proposes a model-reduction methodology that both preserves Lagrangian structure and leads to computationally inexpensive models, even in the presence of high-order nonlinearities. We focus on parameterized simple mechanical systems under Rayleigh damping and external forces, as structural-dynamics models often t this description. The proposed model-reduction methodology directly approximates the quantities that dene the problem’s Lagrangian structure: the Riemannian metric, the potential-energy function, the dissipation function, and the external force. These approximations preserve salient properties (e.g., positive deniteness), behave similarly to the functions they approximate, and ensure computational eciency. Results applied to a simple parameterized trussstructure problem demonstrate the importance of preserving Lagrangian structure and illustrate the method’s ability to generate speedups while maintaining observed stability, in contrast with other model-reduction techniques that do not preserve structure.

Within the context of Liénard equations, we present the FitzHugh--Nagumo model with an idealized nonlinearity. We give an analytical expression (i) for the transient regime corresponding to the emission of a finite number of action potentials (or spikes), and (ii) for the asymptotic regime corresponding to the existence of a limit cycle. We carry out a global analysis to study periodic solutions, the existence of which is linked to the solutions of a system of transcendental equations. The periodic solutions are obtained with the help of the harmonic balance method or as limit behavior of the transient regime. We show how the appearance of periodic solutions corresponds either to a fold limit cycle bifurcation or to a Hopf bifurcation at infinity. The resultsobtained are in agreement with local analysis methods, i.e., the Melnikov method and the averaging method. The generalization of the model leads us to formulate two conjectures concerning the number of limit cycles for the piecewise linear Liénard equations.

We present new methods of analyzing the dynamics of a competitive neural system with different time scales: the K-monotone system theory developed by Kamke (1932) as a global analysis techniques, and the theory of singular perturbation as a local analysis method.

A simplified strategy for force finding analysis of suspendomes

The article presents a finite element based study of linear and geometrically non-linear progressive failure analysis of thin walled composite aerospace structures subjected to combined in-plane and out-of-plane loading which are typically encountered in thin walled aerospace structures. Different ply and constituent based failure criteria and material property degradation schemes have been coded into a PCL code in Nastran. As case studies, progressive failure analyses of sample composite laminates with cut-outs under combined loading are executed to study the effect of geometric non-linearity on the first ply failure and progression of failure. Different ply and constituent based failure criteria and different material property degradation schemes are also compared in terms of predicting the first ply failure and failure progression. For mode independent failure criteria, a method is proposed for the determination of separate degradation factors for fiber and matrix failures which are assumed to occur simultaneously. The results of the present study, show that under combined out-of-plane and in-plane loading, depending on the load case linear analysis can significantly underestimate or overestimate the failure progression compared to geometrically non-linear analysis even at low levels of out-of-plane loading.

Abstract. In this study, we employ low and high-fidelity finite beam elements to conduct geometrical nonlinear transient analyses of composite and sandwich structures. The equations of motion for various structural theories are derived in a total Lagrangian scenario using the Carrera Unified Formulation. The unified formalism's three-dimensional nature enables us to include all components of the Green-Lagrange strain tensor. To solve the equations, we utilize the Hilber-Hughes-Taylor (HHT)-α algorithm in conjunction with a Newton-Raphson procedure. We present the dynamic response of a sandwich stubby beam subjected to a step load, calculated using both equivalent-single layer and layer-wise approaches. Additionally, we discuss the effects of geometrical nonlinearity.

In last years researchers preferred behavior‐based design of structure to force‐based one for designing and construction of the earthquake‐resistance structures, this method is named performance based designing. The main goal of this method is designing of structure members for a certain performance or behavior. On the other hand in most of buildings, load bearing frames are infilled with masonry materials which leads to considerable changes in mechanical properties of frames. But usually infilling wall's effect has been ignored in nonlinear analysis of structures because of complication of the problem and lack of simple logical solution. As a result lateral stiffness, strength, ductility and performance of the structure will be computed with less accuracy. In this paper by use of Smooth hysteretic model for masonry infillings, some high ductile RC frames (4, 8 stories including 1, 2 and 3 spans) designed according to Iranian code are considered. They have been analyzed by nonlinear dynamic method in two states, with and without infilling. Then their performance has been determined with criteria of ATC 40 and compared with recommended performance in Iranian seismic code (standard No. 2800).