Search

The aim of this paper is to develop a robust layer-wise theory for structural analysis of curved glass and photovoltaic panels. By the analogy to the existing theories of plates, governing equations for doubly curved layers including kinematic relations, equilibrium conditions and constitutive equations are introduced. Applying assumptions of shear rigidity of skin layers and moments-free core layer as well as approximations of thin shallow shell, a reduced form of governing differential equations is proposed. Compared to the classical theories of shells the derived system includes an additional second order differential equation. As a result, additional boundary conditions should be satisfied for any edge of the shell. The importance of these extensions is demonstrated for long cylindrical panel with for two examples of simple supports: one with free edges, where relative in-plane displacements of skins are allowed, and one with framed edges, where cross-section rotations of all layers are assumed the same. For both cases closed-form analytical solutions related to a shell strip approximation are presented. Displacement bounds in monolithic and layered cases are derived, and the dependence of deformation and stress characteristics on the radius of curvature and types of supports are illustrated. [ABSTRACT FROM AUTHOR]

In the present work, the flexomagnetic (FM) behaviour of a vibrating squared multi-physic beam in finite dimensions. It is assumed that the bending and shear deformations cause rotary inertia. In the standard type of the Timoshenko beam the rotary inertia originated from shear deformations has been typically omitted. It means the rotary inertia resulting from shear deformation is a new concept considered here. Thus, the novelty in this work is that the effect of shear deformation's rotary inertia (SDRI) on the FM response will be considered in detail. When it comes to nanosize, the well-posed nonlocal elasticity assumption of Eringen can be worth choosing. In this study, the weak form (differential) of strain-driven nonlocal theory is taken into hand for easiness. The procedure of solution will be in regard to the advantage of the Galerkin weighted residual technique based on an analytical flow for the meta beam located at simply-simply supported ends. Several separate studies will show how SDRI and FM can influence each other. The observations give some new achievements in the series of studies on FM. It has been earned that the SDRI can directly impress the flexomagnetic feature of small-scale actuators. [ABSTRACT FROM AUTHOR]

Abstract: Laminated plates with glass skin layers and a core layer from soft polymers are widely used in the civil engineering. Photovoltaic panels currently available on the market are composed from stiff front and back layers and a solar cell layer embedded in a soft polymeric encapsulant. In this paper a layer-wise theory for the structural analysis of glass and photovoltaic laminates is developed. Starting from governing equations for individual layers, kinematical constraints and appropriate interaction forces, a twelfth order system of partial differential equations is derived. The primary variables in the theory include the Airy stress function, the deflection function and the vector of relative in-plane displacements of skin layers. For symmetric laminates a system of uncoupled differential equations with respect to scalar potentials is presented. Three of them correspond to the first order shear deformation plate. The new additional second order differential equation provides a correction function according to the layer-wise theory. Closed form analytical solutions for a plate strip are derived to illustrate the essential influence of this correction for laminates with soft core layer. The importance of additional boundary conditions is shown for examples of free and framed plate edges. [Copyright &y& Elsevier]

In this paper a direct non-local peridynamics theory for thin plates is developed. Peridynamic points are assumed to behave like rigid bodies with independent translation and finite rotation degrees of freedom. The non-local mechanical interaction between points is characterized by force and moment vectors. The balance equations including the linear momentum, the angular momentum and the energy are presented. Peridynamic deformation states of the plate are introduced including the actual bond vector (relative translation of two points within the bond) and the relative finite rotation tensor (actual relative orientation of two points in the bond). The corresponding power-conjugate bond force and bond moment states are derived. The framework to develop constitutive equations for the plate peridynamic states is addressed. Special cases of the theory including plates with zero drilling moments, membranes, soft interlayers as well as stiff plate layers with small relative rotations are considered. [ABSTRACT FROM AUTHOR]

Our analysis incorporates the geometrically nonlinear bending of the Euler-Bernoulli ferromagnetic nanobeam accounting for a size-dependent model through assuming surface effects. In the framework of the flexomagnetic phenomenon, the large deflections are investigated referring to von-Kármán nonlinearity. Employing the nonlocal effects of stress coupled to the gradient of strain generates a scale-dependent Hookean stress–strain scheme related to the small scale. Taking into account the supports of the nanobeam in two cases, that is, totally fixed and hinged, the deformations are predicted. A constant static lateral load is postulated uniformly along the length of the beam, which forces the deformation. As the analysis is based on the one-dimensional media, the electrodes are embedded so that they give off a transverse magnetic field creating a longitudinal force. The newly developed mathematical model is computed by means of the differential quadrature method together with the Newton-Raphson technique. The computational section discusses and reveals the numerical results in detail for the characteristics and parameters involved in the design of beam-like magnetic nanosensors. As shown later, the conducted research presents that there is a strong linkage between the surface effect and the flexomagneticity behavior of the bulk. [ABSTRACT FROM AUTHOR]

In this paper, the equation governing the buckling of a magnetic composite nanoplate under the influence of an in-plane one-dimensional magnetic field, assuming the concept of flexomagnetic and considering the resulting flexural force and moment, is investigated for the first time by different analytical boundary conditions. To determine the equation governing the stability of the nanoplate, the nonlocal strain gradient theory has been used by taking into account the classical plate theory. The axial magnetic force, which is originated from the magnetic field, is investigated. After extracting the governing differential equation, the critical buckling load is obtained for different support conditions. The effect of nonlocal parameter, sheet aspect ratio and the effect of one-dimensional magnetic field on critical load are discussed. It was earned that if the nanoplate is rectangular so that the value of aspect ratio is less than one, the flexomagnetic response will be more noticeable. [ABSTRACT FROM AUTHOR]

A drawback to the material composition of thick functionally graded materials (FGM) beams is checked out in this research in conjunction with a novel hyperbolic-polynomial higher-order elasticity beam theory (HPET). The proposed beam model consists of a novel shape function for the distribution of shear stress deformation in the transverse coordinate. The beam theory also incorporates the stretching effect to present an indirect effect of thickness variations. As a result of compounding the proposed beam model in linear Lagrangian strains and variational of energy, the system of equations is obtained. The Galerkin method is here expanded for several edge conditions to obtain elastic critical buckling values. First, the importance of the higher-order beam theory, as well as stretching effect, is assessed in assorted tabulated comparisons. Next, with validations based on the existing and open literature, the proposed shape function is evaluated to consider the desired accuracy. Some comparative graphs by means of well-known shape functions are plotted. These comparisons reveal a very good compliance. In the final section of the paper, based on an inappropriate mixture of the SUS304 and Si 3 C 4 as the first type of FGM beam (Beam-I) and, Al and Al 2 O 3 as the second type (Beam-II), the results are pictured while the beam is kept in four states, clamped–clamped (C–C), pinned–pinned (S–S), clamped-pinned (C–S) and in particular cantilever (C–F). We found that the defect impresses markedly an FGM beam with boundary conditions with lower degrees of freedom. [ABSTRACT FROM AUTHOR]

In the present study, a single general formulation has been presented for the analysis of various shell-shaped structures. The proposed model is comprehensive and a variety of theories can be used based on it. The cross-section of the shell structure can be arbitrarily analyzed with the presented equations. In other words, various types of shell structures, including cylindrical, conical, spherical, elliptical, hyperbolic, parabolic, and any non-geometric structure with functional cross-section, can be modeled mechanically with only one partial differential equation system. The obtained equations have been solved by applying SAPM semi-analytical solution method. In order to present a comprehensive research, dynamic nonlinear analysis is considered. The variation of material properties through the thickness has been assumed as functionally graded and its effect on the strength of the shell structure with the functional cross-section has been investigated. The numerical results have been compared with available papers and also with FEM results for some structures that there is no paper available for validation. Different types of shell structures have been studied in terms of cross-sectional shape and properties. Finally, the effects of some important factors on the results such as boundary conditions, nonlinear analysis, dynamic analysis, and rotation of the structure around its central axis have been conducted thoroughly. This study and its original governing equations can be considered as a comprehensive reference for mechanical analysis of various shell structures with functional cross-sectional shape. [ABSTRACT FROM AUTHOR]