1,721,152 research outputs found
Eigen-vibrations of Plates made of Functionally Graded Material
Full text linkWithin the framework of the direct approach to the plate theory we consider natural oscillations of plates made of functionally graded materials taking into account both the rotatory inertia and the transverse shear stiffness. It is shown that in some cases the results based on the direct approach differ significantly from the classical estimates. The reason for this is the non-classical computation of the transverse shear stiffness
Vibration Analysis of Non-linear 6-parameter Prestressed Shells
No full textWithin the framework of the nonlinear six-parameter shell theory we discuss the influence of initial (residual) stresses on the eigen-frequencies. We derive the linearized boundary-value problems and formulate the Rayleigh variational principle which gives the possibility to estimate the eigen-frequencies of the prestressed shell. The Rayleigh quotient of the shell with initial stresses is represented as a sum of two terms. The first term depends on elastic moduli of the shell while the second one is determined by initial stress and couple stress tensors acting on the shell
On the linear theory of micropolar plates
No full textWe discuss the general linear six-parametric theory of plates based on the direct approach. We consider the plate as a deformable surface. Each material point of the surface can be regarded as an infinitesimal small rigid body with six degrees of freedom. The kinematics of the plate is described by using the vector of translation and the vector of rotation as the independent variables. The relations between the equilibrium conditions of a three-dimensional micropolar plate-like body and the two-dimensional equilibrium equations of the deformable surface are established. Using the three-dimensional constitutive equations of a micropolar material we discuss the determination of the effective stiffness tensors appearing in the two-dimensional constitutive equations
Generalized continua with applications: Euromech Solid Mechanics Conference 2018
No full textMotivating by two minisymposia on generalized models of continua organized within the Euromech Solid Mechanics Conference, Bologna, Italy 2018, we introduce the corresponding special issue based on these events
Direct approach-based analysis of plates composed of functionally graded materials
No full textThe classical plate theory can be applied to thin plates made of classical materials like steel. The first theory allowing the analysis of such plates was elaborated by Kirchhoff. But this approach was connected with various limitations (e.g., constant material properties in the thickness direction). In addition, some mathematical inconsistencies like the order of the governing equation and the number of boundary conditions exist. During the last century many suggestions for improvements of the classical plate theory were made. The engineering direction of improvements was ruled by applications (e.g., the use of laminates or sandwiches as the plate material), and so new hypotheses for the derivation of the governing equations were introduced. In addition, some mathematical approaches like power series expansions or asymptotic integration techniques were applied. A conceptional different direction is connected with the direct approach in the plate theory. This paper presents the extension of Zhilin's direct approach to plates made of functionally graded materials
On the constitutive equations of viscoelastic micropolar plates and shells of differential type
No full textWithin the framework of the micropolar theory of continuum we discuss the constitutive equations of viscoelastic micropolar thin-walled structures, i.e. viscoelastic micropolar plates and shells. Starting from the linear viscoelastic micropolar continuum and using the correspondence principle of the linear viscoelasticity we extend the procedure of reduction of three-dimensional equilibrium equations of elastic shell-like solids to the case of viscoelastic behavior. We restricted ourselves by constitutive equations of differential type. In other words, we consider both 2D and 3D constitutive equations which are linear dependencies between certain set of time derivatives of stress and strain measures
On the bending of viscoelastic plates made of polymer foams
No full textConsidering the viscoelastic behavior of polymer foams a new plate theory based on the direct approach is introduced and applied to plates composed of functionally graded materials (FGM). The governing two-dimensional equations are formulated for a deformable surface, the viscoelastic stiffness parameters are identified assuming linear-viscoelastic material behavior. The material properties are changing in the thickness direction. Solving some problems of the global structural analysis it will be demonstrated that in some cases the results significantly differ from the results based on the Kirchhoff-type theory
Equilibrium of a second-gradient fluid and an elastic solid with surface stresses
No full textWe discuss the kinematical compatibility conditions describing interaction of a second-gradient fluid with an elastic solid possessing the surface elasticity properties
Strain rate tensors and constitutive equations of inelastic micropolar materials
No full textNonlinear micropolar continuum model allows to describe complex micro-structured media, for example, polycrystals, foams, cellular solids, lattices, masonries, particle assemblies, magnetic rheological fluids, liquid crystals, etc., for which the rotational degrees of freedom of material particles are important. The constitutive equations of the hyperelastic nonlinear micropolar continuum can be expressed using the strain energy density depending on two strain measures. In the case of inelastic behavior the constitutive equations of the micropolar continuum have more complicated structure, the stress and couple stress tensors as well as other quantities depend on the history of strain measures. In what follows we discuss the constitutive equations of the nonlinear micropolar continuum using strain rates
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