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This study aims to simulate gust effects on the aeroelastic behavior of a flexible aircraft. The dynamic response of the system for different discreet gust excitations is obtained using numerical simulations.

Coupled dynamics, including rigid and flexible body coordinates, are considered for modeling the dynamic behavior of the aircraft. Wing is considered flexible and other parts are considered rigid. Wing is modeled with nonlinear Euler Bernoulli beam. Moreover, unsteady aerodynamics based on the Wagner function are used for aerodynamic loading, and the results are compared with those of quasi-steady aerodynamics.

Von Kármán continuous gust is applied to this aircraft. In addition, the discrete “1- cosine” gust with different gust lengths is applied to the aircraft, and the maximum and minimum accelerations are computed. It is shown that the nonlinear modeling of the system represents the actual behavior and causes limit cycle oscillation phenomena.

This methodology can yield a relatively simple dynamic model for high aspect ratio aircrafts to provide insights into the vehicles’ dynamics, which can be available early in the design cycle.

The purpose of this paper is to extend a recent unsymmetric 8-node, 24-DOF hexahedral solid element US-ATFH8 with high distortion tolerance, which uses the analytical solutions of linear elasticity governing equations as the trial functions (analytical trial function) to geometrically nonlinear analysis.

Based on the assumption that these analytical trial functions can still properly work in each increment step during the nonlinear analysis, the present work concentrates on the construction of incremental nonlinear formulations of the unsymmetric element US-ATFH8 through two different ways: the general updated Lagrangian (UL) approach and the incremental co-rotational (CR) approach. The key innovation is how to update the stresses containing the linear analytical trial functions.

Several numerical examples for 3D structures show that both resulting nonlinear elements, US-ATFH8-UL and US-ATFH8-CR, perform very well, no matter whether regular or distorted coarse mesh is used, and exhibit much better performances than those conventional symmetric nonlinear solid elements.

The success of the extension of element US-ATFH8 to geometrically nonlinear analysis again shows the merits of the unsymmetric finite element method with analytical trial functions, although these functions are the analytical solutions of linear elasticity governing equations.

Gives a bibliographical review of the finite element methods (FEMs) applied for the linear and nonlinear, static and dynamic analyses of basic structural elements from the theoretical as well as practical points of view. The range of applications of FEMs in this area is wide and cannot be presented in a single paper; therefore aims to give the reader an encyclopaedic view on the subject. The bibliography at the end of the paper contains 2,025 references to papers, conference proceedings and theses/dissertations dealing with the analysis of beams, columns, rods, bars, cables, discs, blades, shafts, membranes, plates and shells that were published in 1992‐1995.

The purpose of this paper is to present a simple HP-cloud method as an accurate meshless method for the geometrically nonlinear analysis of thick orthotropic plates of general shape. This method is used to investigate the effects of thickness, geometry of various shapes, boundary conditions and material properties on the large deformation analysis of Mindlin plates.

Nonlinear analysis of plates based on Mindlin theory is presented. The equations are derived by the Von-Karman assumption and total Lagrangian formulations. Newton-Raphson method is applied to achieve linear equations from nonlinear equations. Simple HP-cloud method is used for the construction of the shape functions based on Kronecker-δ properties, so the essential boundary conditions can be enforced directly. Shepard function is utilized for a partition of unity and complete polynomial is used as an enrichment function.

The suitability and efficiency of the simple HP-cloud method for the geometrically nonlinear analysis of thin and moderately thick plates is studied for the first time. Large displacement analysis of various shapes of plates, rectangular, skew, trapezoidal, circular, hexagonal and triangular with different boundary conditions subjected to distributed loading are considered.

This paper shows that the simple HP-cloud method is well suited for the large deformation analysis of Mindlin plates with various geometries, because it uses a set of a few arbitrary nodes placed in a plate of general shape. Moreover the convergence rate of the proposed method is high and the cost of solving equations is low.

The purpose of this paper is to propose an efficient and accurate numerical model that employs isogeometric analysis (IGA) for the geometrically nonlinear analysis of functionally graded plates (FGPs). This model is utilized to investigate the effects of boundary conditions, gradient index, and geometric shape on the nonlinear responses of FGPs.

A geometrically nonlinear analysis of thin and moderately thick functionally graded ceramic-metal plates based on IGA in conjunction with first-order shear deformation theory and von Kármán strains is presented. The displacement fields and geometric description are approximated with nonuniform rational B-splines (NURBS) basis functions. The Newton-Raphson iterative scheme is employed to solve the nonlinear equation system. Material properties are assumed to vary along the thickness direction with a power law distribution of the volume fraction of the constituents.

The present model for analysis of the geometrically nonlinear behavior of thin and moderately thick FGPs exhibited high accuracy. The shear locking phenomenon is avoided without extra numerical efforts when cubic or high-order NURBS basis functions are utilized.

This paper shows that IGA is particularly well suited for the geometrically nonlinear analysis of plates because of its exact geometrical modelling and high-order continuity.

The purpose of this paper is to evaluate the capabilities of the generalized finite element method (GFEM) under the context of the geometrically nonlinear analysis. The effect of large displacements and deformations, typical of such analysis, induces a significant distortion of the element mesh, penalizing the quality of the standard finite element method approximation. The main concern here is to identify how the enrichment strategy from GFEM, that usually makes this method less susceptible to the mesh distortion, may be used under the total and updated Lagrangian formulations.

An existing computational environment that allows linear and nonlinear analysis, has been used to implement the analysis with geometric nonlinearity by GFEM, using different polynomial enrichments.

The geometrically nonlinear analysis using total and updated Lagrangian formulations are considered in GFEM. Classical problems are numerically simulated and the accuracy and robustness of the GFEM are highlighted.

This study shows a novel study about GFEM analysis using a complete polynomial space to enrich the approximation of the geometrically nonlinear analysis adopting the total and updated Lagrangian formulations. This strategy guarantees the good precision of the analysis for higher level of mesh distortion in the case of the total Lagrangian formulation. On the other hand, in the updated Lagrangian approach, the need of updating the degrees of freedom during the incremental and iterative solution are for the first time identified and discussed here.

The purpose of this paper is to present an efficient smoothed particle hydrodynamics (SPH) method particularly adapted for the geometrically nonlinear analysis of structures.

In order to resolve the inconsistency phenomenon which systematically occurs in the standard SPH method at the domain’s boundaries of the studied structure, the classical kernel function and its spatial derivatives were modified by the use of Taylor series expansion. The well-known tensile instabilities inherent to the Eulerian SPH formulation were attenuated by the use of the Total Lagrangian Formulation (TLF).

In order to demonstrate the effectiveness of the present improved SPH method, several numerical applications involving geometrically nonlinear behaviors were carried out using the explicit dynamics scheme for the time integration of the PDEs. Comparisons of the obtained results using the present SPH model with analytical reference solutions and with those obtained using ABAQUS finite element (FE) commercial software, show its good accuracy and robustness.

An additional application including a multilayered composite structure and involving buckling and delamination was investigated using the present improved SPH model and the results are compared to the FE results, they confirmed both the efficiency and the accuracy of the proposed method.

An efficient 2D-continuum SPH model for the geometrically nonlinear analysis of thin and thick structures is proposed. Contrarily to the classical SPH approaches, here the constitutive material relations are used to link naturally the stresses and strains. The Total Lagrangian approach is investigated to alleviate the tensile instabilities problem, allowing at the same time to avoid the updating procedure of the neighboring particles search and therefore reducing CPU usage. The proposed approach is valid for isotropic and multilayered composites structures undergoing large transformations. CPU time savings and better results with the new 2D-continuum SPH formulation compared to the classical continuum SPH. The explicit dynamic scheme was used for time integration allowing a fast resolution algorithm even for highly nonlinear problems.

This article presents a geometrically non-linear finite element formulation for the analysis of planar two-layer beam-columns taking into account the inter-layer slip and uplift.

The co-rotational method is adopted, in which the motion of the element is decomposed into a rigid body motion and a small deformational one. The geometrically linear formulation can be used in the local frame and automatically be transformed into a geometrically nonlinear one. In co-rotational frame, both layers are assumed to be discretely connected at the element ends. Slips and uplifts are assumed to be small. Consequently, the condition of non interpenetration between the layers can be treated using a node-to-node contact algorithm. The resolution methods such as penalty (PM) and augmented Lagrangian method (ALM) with Uzawa updating scheme can be used.

The non-penetration condition between the layers of composite beams can be formulated by using contact law. It is found that despite a low convergence rate of augmented Lagrangian method compared to penalty method, the former prevents the unrealistic penetration. Besides, it is shown that the buckling load of the composite beam-column is largely affected by the uplift stiffness of the connectors.

The proposed finite element model is capable of simulating accurately the geometrically non-linear behavior of planar two-layer beam-columns taking into account the inter-layer slip and uplift. Regarding uplift, the non-penetration condition is strictly enforced by considering rigorous contact conditions at the interface. The constraint problem is solved using the penalty method or the augmented Lagrangian method with the Uzawa updating scheme.

The purpose of this study is dedicated to use an efficient mixed strain finite element approach to develop a three-node triangular shell element. Moreover, large deformation analysis of the functionally graded material shells is the main contribution of this research. These target structures include thin or moderately thick panels.

Due to reach these goals, Green–Lagrange strain formulation with respect to small strains and large deformations with finite rotations is used. First, an efficient three-node triangular degenerated shell element is formulated using tensorial components of two-dimensional shell theory. Then, the variation of Young’s modulus through the thickness of shell is formulated by using power function. Note that the change of Poisson’s ratio is ignored. Finally, the governing linearized incremental relation was iteratively solved using a high potential nonlinear solution method entitled generalized displacement control.

Some well-known problems are solved to validate the proposed formulations. The suggested triangular shell element can obtain the exact responses of functionally graded (FG) shell structures, without any shear locking, instabilities and ill-conditioning, even by using fewer numbers of the elements. The obtained outcomes are compared with the other reference solutions. All findings demonstrate the accuracy and capability of authors’ element for analyzing FG shell structures.

A mixed strain finite element approach is used for nonlinear analysis of FG shells. These structures are curved thin and moderately thick shells. Small strains and large deformations with finite rotations are assumed.

FG shells are mostly made curved thin or moderately thick, and these structures have a lot of applications in the civil and mechanical engineering.

The social implication of this study is concerned with how technology impacts the world. In short, the presented scheme can improve structural analysis ways.

Developing an efficient three-node triangular element, for geometrically nonlinear analysis of FG doubly-curved thin and moderately thick shells, is the main contribution of the current research. Finite rotations are considered by using the Taylor’s expansion of the rotation matrix. Mixed interpolation of strain fields is used to alleviate the locking phenomena. Using fewer numbers of shell elements with fewer numbers of degrees of freedom can reduce the computational costs and errors significantly.

The purpose of this paper is to analyse the nonlinear flexural behaviour of laminated curved panel under uniformly distributed load. The study has been extended to analyse different types of shell panels by employing the newly developed nonlinear mathematical model.

The authors have developed a novel nonlinear mathematical model based on the higher order shear deformation theory for laminated curved panel by taking the geometric nonlinearity in Green-Lagrange sense. In addition to that all the nonlinear higher order terms are considered in the present formulation for more accurate prediction of the flexural behaviour of laminated panels. The sets of nonlinear governing equations are obtained using variational principle and discretised using nonlinear finite element steps. Finally, the nonlinear responses are computed through the direct iterative method for shell panels of various geometries (spherical/cylindrical/hyperboloid/elliptical).

The importance of the present numerical model for small strain large deformation problems has been demonstrated through the convergence and the comparison studies. The results give insight into the laminated composite panel behaviour under mechanical loading and their deformation behaviour. The effects of different design parameters and the shell geometries on the flexural responses of the laminated curved structures are analysed in detailed. It is also observed that the present numerical model are realistic in nature as compared to other available mathematical model for the nonlinear analysis of the laminated structure.

A novel nonlinear mathematical model is developed first time to address the severe geometrical nonlinearity for curved laminated structures. The outcome from this paper can be utilized for the design of the laminated structures under real life circumstances.