Geometrically Nonlinear Theory of Multilayered Plates with Interlayer Slips

Geometrically nonlinear theory of multilayered plates with interlayer slips

A refined asymptotic theory and computational model for multilayered composite plates

A system of solving equations of the problem of dynamics of multilayer shells and boundary conditions are derived by the variational method on the basis of relationships of a dynamic model of the stress-strain state. Comparison of results of the solution of characteristic problems with the three-dimensional solution indicated that in terms of accuracy, they are higher than those of certain familiar theories, the hypotheses of which, in contrast to the proposed theory, disregard such a dynamic factor as inertial forces.

Variant of the nonclassical theory of multilayer shallow shells and plates

In this paper, an accurate and efficient C0-type third-order global---local model incorporating effects of the transverse normal strain is proposed to study the thermal/mechanical behaviors of thick multilayer cross-ply plates. Transverse displacement is assumed to be a linear distribution through the thickness direction, for which the normal strain could be readily computed. Based on the interlaminar continuity conditions of in-plane displacement and transverse shear stresses, layer-dependent variables could be reduced. Employing shear stress free condition at the upper and the lower surfaces, derivatives of transverse displacement are eliminated from the displacement field, so that C0 interpolation functions are only required for the finite element implementation. As a result, the number of variables is independent of the number of layers of the laminate. To assess the proposed model, the classical quadratic eight-node isoparametric element is used for the interpolation of all the displacement parameters defined at each nodal point on the composite plate. Comparing with various existing composite plate models, it is found that simple C0 finite elements with non-zero normal strain could produce accurate deformations and stresses of thick multilayer composite plates subjected to thermal and mechanical loads.

High-order theory for the analysis of multi-layer plate assemblies and its application for the analysis of sandwich panels with terminating plies

On a nonlinear theory of plates and shells including consistent and inconsistent kinematics and the finite element method

Flutter is one of the most known instability phenomena. This condition occurs when a given structure exhibits sustained, harmonic oscillations, sometimes leading to catastrophic events. The prediction of flutter represents a crucial point for a correct and safe design. When fluid structure interactions produce dynamic instability, flutter analyses require accurate descriptions of body deformations and aerodynamic loads. To this end, aerodynamic theories have been coupled with structural models to develop aeroelastic analysis tools, whose reliability is the results of a trade-off between the accuracy and the computational efficiency. From a computational point of view, the most efficient formulation is based on the 1D assumption, where the problem is reduced to a set of variables that only depends on the beam-axis coordinate. Besides the well-known classical beam theories, several refined kinematic models have been proposed, to study the stability of rotating blades and shafts. However, when these structures are highly deformable or the material distribution involves non-classical structural couplings, 2D and 3D solutions are still required. Within this work, we propose an advanced 1D formulation to analyse the stability of rotating structures. The higher-order beam theories are obtained using the Carrera Unified Formulation (CUF), which allows to derive, at least theoretically, an infinite number of kinematic models. The Equations of Motion (EoM) for shafts and blades include the Coriolis term and the centrifugal effects (spin softening and geometrical stiffening). For the subsonic flow regime, aerodynamic loads are defined following the unsteady strip theories proposed by Theodorsen and Loewy. For the supersonic regime, the linear Piston theory is extended to structures rotating in compressed air flow. The Finite Element Method (FEM) is used to solve the weak form of the EoM. Firstly, to evaluate the accuracy of 1D CUF elements, static and free-vibration analysis are carried out on compact and thin-walled structures of isotropic, orthotropic and functionally graded materials. Then, higher-order elements are used to study the dynamics of laminated shafts, thin cylinders, discs and blades, which rotate about the longitudinal and transverse axis. Results show the improved performance of the 1D CUF theories compared to 2D and 3D solutions. In order to evaluate the proposed aeroelastic formulation, we test different wing configurations, including thin-walled box beams. The effects of the sweep angle and the lamination scheme on flutter conditions are evaluated, and results are compared with plate solutions, experimental tests and aeroelastic analysis carried out with the Doublet Lattice Method (DLM). Moreover, comparisons between Theodorsen and Loewy aerodynamic theories are presented for a realistic rotary-wing model. In the last numerical examples, the linear Piston Theory is used to describe the dynamics of thin plates with different aspect-ratio surrounded by compressed air. For this cases, results are compared with an existing solution based on a non-linear plate theory

Initial rotational stiffness of end-plate connections based on the theory of plates and shells

Nonlinear forced vibration of simply supported functionally graded porous nanocomposite thin plates reinforced with graphene platelets

Theory of elastic plates in the reference state

Computer simulation of the bending of a rectangular multilayer plate using a numerical approach is carried out on the basis of differential equations of a variant of the refined theory of multilayer plates, which take into account: transverse shear, pressure of layers against each other, normal deformations, layer orthotropy, asymmetry of the structure. The general order of the system is 12. Three functions of the coordinate surface are unknown: the function of effort, deflection, and shear. The boundary conditions for various cases of fixing the edges of the plate are obtained from the contour integral of the variational equation. Discretization of the system of resolving equations and the corresponding contour conditions for a computer simulation of the bending of a rectangular multilayer plate was performed by the finite difference method. According to the proposed numerical technique on the basis of a two-dimensional model, computer simulation of the problem of bending three-layer articulated support symmetrical in thickness square plates with orthotropic carbon fiber layers in a wide range of changes was carried out.

In this paper, moderately large deflections of beams with interlayer slip subjected to lateral loads are analyzed. The considered beams are composed of three elastically bonded layers, which are symmetrically disposed about the central axis. The displacements of the hinged supports are fully restrained, and thus, the response becomes geometrically nonlinear. The structural model utilized to analyze the beams is based on a layerwise application of the Euler-Bernoulli kinematic assumptions, a linear interlaminar slip law, and a nonlinear axial strain-displacement relation. The results of an application example demonstrate the grave effect of interlayer slip on the nonlinear deflection of layered beams.

This review article is devoted to the use of the Reissner Mixed Variational Theorem (RMVT) forward two-dimensional modeling of flat and curved, multilayer structures. A thorough review of the literature involving the use in the modeling of multilayered plates and shells using RMVT is also presented. In the first part, the paper overviews relevant key points that should be taken into account for an accurate description of strain and stress fields in multilayered plate and shell analysis. It is then shown that RMVT has been originated in view of the fulfillment of such key points, herein referred to as C0-Requirements (zig-zag form of the displacement fields in the thickness direction and continuity of transverse normal and shear stresses at each layer interface). Classical variational statements are used to introduce Reissner’s Theorem. In the second part, the paper presents various ways in which RMVT can be used to develop plate and shell theories in a systematic manner. The so called layer-wise and equivalent single layer variable description are considered. Both strong and weak (finite element) forms of governing equations have been derived. A Weak Form of Hooke’s Law (WFHL), is also discussed as an idea to eliminate transverse stress variables leading to standard classical models with only displacement unknowns. Two appendices display details of governing equations related to multilayered doubly curved shells and to finite element matrices of multilayered plates. A third part reviews the works that have appeared in literature which make use of RMVT. Mainly papers on multilayered plate and shell modelings have been addressed. The final part of the paper is devoted to giving an overview with selected results of numerical performance that can be acquired by RMVT applications; extensive comparison to elasticity solutions and to other significant analyses, based on classical and refined approaches, are given. It is concluded that Reissner’s Mixed Theorem should be considered as a natural tool for multilayered structure analyses; it plays a similar role to that of the Principle of Virtual Displacement in the analysis of isotropic single-layer structures. This review article includes 119 references.

Finite strip elements for laminated composite plates with transverse shear strain discontinuities