Explore the vast range of titles available.

An iterative algorithm is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the nth approximation is derived from the previous ones. As a first endeavor, the nonlinear dynamic instability performance of the electrical plate on the nonlinear elastic substrate using an iterative algorithm is scrutinized in this research. A nonlinear elastic foundation is assumed to be in contact with the electrical plate during deformation. The nonlinear coupled dynamic equations governing the transverse and longitudinal motions of the electrical plate are derived using Hamilton’s principle method, the von Kármán geometric nonlinearity, and improved higher-order shear deformation theory. The iterative algorithm based generalized differential quadrature method (IAB-GDQM) is applied for solving the nonlinear equations with the aid of nonlinear boundary domains. Parametric studies are implemented to explore the impacts of the applied voltage, geometry of the plate, and nonlinear factor on large amplitude motion, and nonlinear dynamics of the presented system for various boundary domains. Results show that the nonlinear dynamic depends on nonlinear elastic foundation effects and the applied voltage, which can be used to design the electrically structures in different environmental conditions accurately.

The direct parametrisation method for invariant manifolds is used for model order reduction of forced-damped mechanical structures subjected to geometric nonlinearities. Nonlinear mappings are introduced, allowing one to pass from the degrees of freedom of the finite-element model to the normal coordinates. Arbitrary orders of expansions are considered for the unknown mappings and the reduced dynamics, which are then solved sequentially through the homological equations for both autonomous and time-dependent terms. It is emphasised that the two problems share a similar structure, which can be used for an efficient implementation of the non-autonomous added terms. Special emphasis is also put on the new resonance conditions arising due to the presence of the external forcing frequencies, which allow predicting phenomena such as parametric excitation and isolas formation. The method is then applied to structures of academic and industrial interest. First, the large amplitude vibrations of a forced-damped cantilever beam are studied. This example highlights that high-order non-autonomous terms are compulsory to correctly estimate the maximum vibration amplitude experienced by the structure. The birth of isolated solutions is also illustrated on this example. The cantilever is then used to show how quadratic coupling creates conditions for the excitation of the parametric instability, and that this feature is correctly embedded in the reduction process. A shallow arch excited with multi-modal forcing is then studied to detail different forcing effects. Finally, the approach is validated on a structure of industrial relevance, i.e. a comb-driven micro-electro-mechanical resonator. The accuracy and computational performance reported suggest that the proposed methodology can accurately predict the nonlinear dynamic response of a large class of nonlinear vibratory systems.

The article presents the results of a numerical study of the composite action of concrete and reinforcement in reinforced concrete flooring under emergency loads, taking into account physical and geometric nonlinearities. The study used a nonlinear static method in the LS-DYNA software package, which implements the Continuous Surface Cap Model (CSCM). The simulation model of a monolithic beam floor uses volumetric finite elements for concrete and rod elements for reinforcement. Isofields and graphs of the intensity of stresses and strains in the upper and lower reinforcement, as well as in the concrete at the floor elevation, with an increase in the vertical uniformly distributed load, were built. The load-bearing capacity of the monolithic slab under consideration was determined using the non-collapse criterion. The LS-DYNA software package makes it possible to study the action of load-bearing concrete structures modeling direct concrete reinforcement using reinforcing bars at a significantly nonlinear nature of strain.

An evaluation of the commercial transport aircraft developed over the past decades evidences an increasing trend toward the use of high aspect-ratio wings. This trend is justified by the well-known effect of slender wings in reducing fuel consumption, leading to lower operational costs and a milder environmental impact. There are many studies about the effects of geometric nonlinearities on aeroelastic behavior of very flexible wings in symmetrical maneuvers. However, geometric nonlinearities may also significantly affect the aeroelastic behavior of the wing under non-symmetrical conditions, especially when ailerons are deflected. Within this context, this work presents a static fluid–structure interaction approach to evaluate the rolling characteristics of very flexible wings. First, a modified version of the very flexible Pazy Wing from Aeroelastic Prediction Workshop (AEPW-3) is proposed, now equipped with ailerons. Next, a fluid–structure interaction tool that couples a full potential aerodynamic solver with an implicit nonlinear structural solver is presented to allow simulations of wings with deflected ailerons. The presented method is applied to the modified Pazy wing considering multiple linear and nonlinear structural analyses, for different aileron deflection angles. The results show that when geometric nonlinearity effects are considered, the aileron effectiveness tends to decrease as the structural flexibility increases. On the other hand, if geometric nonlinearities are neglected, the aileron effectiveness falsely enhances as the wing flexibility rises.

The concentration of the current contribution is on the geometrically nonlinear analysis of laminated composite shells employing the finite element method. For this purpose, the use is made of a higher-order shell model with extensible directors possessing twelve parameters, then the exact Green–Lagrange strains and the three-dimensional second Piola–Kirchhoff stress tensor are extracted based on the base vectors of the shell mid-surface. The principle of virtual work is adopted to derive the weak form of governing equations. A computationally efficient four-node shell element is designed and to remedy the locking problems involving transverse shear, membrane and curvature–thickness ones, the ANS (assumed natural strain) approach and the assumed strain scheme are used. Finally, standard benchmarks are solved for isotropic materials allowing geometric nonlinearity to examine the performance of the proposed shell element and then results of thin and thick layered composite structures are presented.

Despite its rapid development, Physics-Informed Neural Network (PINN)-based computational solid mechanics is still in its infancy. In PINN, the loss function plays a critical role that significantly influences the performance of the predictions. In this paper, by using the Least Squares Weighted Residual (LSWR) method, we proposed a modified loss function, namely the LSWR loss function, which is tailored to a dimensionless form with only one manually determined parameter. Based on the LSWR loss function, an advanced PINN technique is developed for computational 2D and 3D solid mechanics. The performance of the proposed PINN technique with the LSWR loss function is tested through 2D and 3D (geometrically nonlinear) problems. Thoroughly studies and comparisons are conducted between the two existing loss functions, the energy-based loss function and the collocation loss function, and the proposed LSWR loss function. Through numerical experiments, we show that the PINN based on the LSWR loss function is effective, robust, and accurate for predicting both the displacement and stress fields. The source codes for the numerical examples in this work are available at https://github.com/JinshuaiBai/LSWR_loss_function_PINN/ .

Large flexible aircraft are often accompanied by large deformations during flight leading to obvious geometric nonlinearities in response. Geometric nonlinear dynamic response simulations based on full-order models often carry unbearable computing burden. Meanwhile, geometric nonlinearities are caused by large flexible wings in most cases and the deformation of fuselages is small. Analyzing the whole aircraft as a nonlinear structure will greatly increase the analysis complexity and cost. The analysis of complicated aircraft structures can be more efficient and simplified if subcomponents can be divided and treated. This paper aims to develop a hybrid interface substructure synthesis method by expanding the nonlinear reduced-order model (ROM) with the implicit condensation and expansion (ICE) approach, to estimate the dynamic transient response for aircraft structures including geometric nonlinearities. A small number of linear modes are used to construct a nonlinear ROM for substructures with large deformation, and linear substructures with small deformation can also be assembled comprehensively. The method proposed is compatible with finite element method (FEM), allowing for realistic engineering model analysis. Numerical examples with large flexible aircraft models are calculated to validate the accuracy and efficiency of this method contrasted with nonlinear FEM.

The present research deals with the nonlinear free vibration responses of laminated composite flat panel under hygrothermal environment, by considering the corrugated material properties of the composite lamina through a micromechanical model. The plate has been modeled in the framework of the higher-order shear deformation theory and Green-Lagrange strain displacement relations have been used to account for the geometric nonlinearity. Moreover, the present formulation incorporates all the nonlinear higher order terms arising in the model to capture the exact flexure of the panel. Hamilton's principle has been adopted to derive the system governing equations and suitable nonlinear finite element steps have been employed for discretization. The responses are computed using direct iterative method and compared with those available published results for validation purpose. Numerical illustrations are presented to investigate the effect of various parameters (thickness ratio, support conditions and lamination scheme) on the nonlinear frequency responses of laminated composite plate under hygrothermal environment using the present model and discussed in details.

This paper aims at reviewing nonlinear methods for model order reduction in structures with geometric nonlinearity, with a special emphasis on the techniques based on invariant manifold theory. Nonlinear methods differ from linear-based techniques by their use of a nonlinear mapping instead of adding new vectors to enlarge the projection basis. Invariant manifolds have been first introduced in vibration theory within the context of nonlinear normal modes and have been initially computed from the modal basis, using either a graph representation or a normal form approach to compute mappings and reduced dynamics. These developments are first recalled following a historical perspective, where the main applications were first oriented toward structural models that can be expressed thanks to partial differential equations. They are then replaced in the more general context of the parametrisation of invariant manifold that allows unifying the approaches. Then, the specific case of structures discretised with the finite element method is addressed. Implicit condensation, giving rise to a projection onto a stress manifold, and modal derivatives, used in the framework of the quadratic manifold, are first reviewed. Finally, recent developments allowing direct computation of reduced-order models relying on invariant manifolds theory are detailed. Applicative examples are shown and the extension of the methods to deal with further complications are reviewed. Finally, open problems and future directions are highlighted.

Origami-inspired designs possess attractive applications to science and engineering (e.g. deployable, self-assembling, adaptable systems). The special geometric arrangement of panels and creases gives rise to unique mechanical properties of origami, such as reconfigurability, making origami designs well suited for tunable structures. Although often being ignored, origami structures exhibit additional soft modes beyond rigid folding due to the flexibility of thin sheets that further influence their behaviour. Actual behaviour of origami structures usually involves significant geometric nonlinearity, which amplifies the influence of additional soft modes. To investigate the nonlinear mechanics of origami structures with deformable panels, we present a structural engineering approach for simulating the nonlinear response of non-rigid origami structures. In this paper, we propose a fully nonlinear, displacement-based implicit formulation for performing static/quasi-static analyses of non-rigid origami structures based on ‘bar-and-hinge’ models. The formulation itself leads to an efficient and robust numerical implementation. Agreement between real models and numerical simulations demonstrates the ability of the proposed approach to capture key features of origami behaviour.