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Within the linear Toupin–Mindlin strain gradient elasticity we discuss the well‐posedness of the first boundary‐value problem, that is, a boundary‐value problem with Dirichlet‐type boundary conditions on the whole boundary. For an isotropic material we formulate the necessary and sufficient conditions which guarantee existence and uniqueness of a weak solution. These conditions include strong ellipticity written in terms of higher‐order elastic moduli and two inequalities for the Lamé moduli. The conditions are less restrictive than those followed from the positive definiteness of the deformation energy. [ABSTRACT FROM AUTHOR]

A study of existence and uniqueness of weak solutions to boundary value problems describing an elastic body with weakly nonlocal surface elasticity is presented. The chosen model incorporates the surface strain energy as a quadratic function of the surface strain tensor and the surface deformation gradients up to Nth order. The virtual work principle, extended for higher‐order strain gradient media, serves as a basis for defining the weak solution. In order to characterize the smoothness of such solutions, certain energy functional spaces of Sobolev type are introduced. Compared with the solutions obtained in classical linear elasticity, weak solutions for solids with surface stresses are smoother on the boundary; more precisely, a weak solution belongs to H1(V)∩HN(Ss) where Ss⊂S≡∂V and V⊂R3. A study of existence and uniqueness of weak solutions to boundary value problems describing an elastic body with weakly nonlocal surface elasticity is presented. The chosen model incorporates the surface strain energy as a quadratic function of the surface strain tensor and the surface deformation gradients up to Nth order. The virtual work principle, extended for higher‐order strain gradient media, serves as a basis for defining the weak solution..... [ABSTRACT FROM AUTHOR]

Three-layer laminates with thin soft core layer can be found in many engineering applications. Examples include laminated glasses and photovoltaic panels. For such structures high contrast in the mechanical properties of faces and core requires the use of advanced methods to determine effective material properties of the laminate. In this paper we address the application of the first order shear deformation plate theory to the analysis of laminates with thin and soft core layer. In particular, transverse shear stiffness parameters for three-layered plates with different symmetric configurations are analyzed. For classical sandwiches with thick core layer the result coincides with the Reissner's formula. For the case of thin and compliant core layer the new expression for the effective shear stiffness is derived. [ABSTRACT FROM AUTHOR]

This paper wants to draw attention to several issues in electrodynamic field theory and to make way for a rational continuum approach to the subject. The starting point are the balances for magnetic flux and electric charge, both in a very general formulation for volumes and for open surfaces, all of which can deform and be immaterial or material. The spatial point‐of‐view for the description of fields is favored and its advantages in comparison to the concept of material particles is explained. A straightforward answer to the question of how to choose units for the electromagnetic fields most suitably is also presented. The transformation properties of the electromagnetic fields are addressed by rewriting the balances in space–time notation. Special attention is paid to the connection between the two sets of electromagnetic fields through the so‐called Maxwell–Lorentz–æther relations. The paper ends with an outlook into constitutive theory of matter under the influence of electromagnetic fields and a discussion on curious developments in context with Maxwell's equations. [ABSTRACT FROM AUTHOR]

The authors reflect the life and career of Iosif Izrailevich-Girshevich Vorovich, a Russian and Soviet mechanist and mathematician. The authors say that Vorovich was born on June 21, 1920 in Bryansk, Soviet Union. The authors mention that he studied at Moscow State University (MSU) and became a military student at the Zhukovsky Air Force Engineering Academy (ZAFEA). Moreover, Vorovich also worked at Rostov State University (RSU).

The mathematical investigation of the initial-boundary and boundary value problems in the linear elasticity considering surface stresses is presented. Weak setup of the problems based on mechanical variational principles is studied. Theorems of uniqueness and existence of the weak solution in energy spaces of static and dynamic problems are formulated and proved. Some properties of the spectrum of the problems under consideration are established. The studies are performed applying the functional analysis techniques. Finally, the Rayleigh principle for eigenfrequencies is constructed. [ABSTRACT FROM AUTHOR]

We 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. [ABSTRACT FROM AUTHOR]

Considering 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 and the stiffness parameters are identified for the linear viscoelastic isotropic material behavior. It is assumed that the material properties are changing in thickness direction. Solving the plate bending problem of the global mechanical analysis, it will be demonstrated that in some cases, the results significantly differ from the results based on the classical Kirchhoff-type theory. [ABSTRACT FROM AUTHOR]

Constitutive inequalities in general static and dynamic theory of elastic shells undergoing finite deformation are discussed. Constitutive inequalities are well known in continuum mechanics. They express physical or mathematical restrictions for constitutive equations of 3D elastic materials. In this paper we discuss the analogs of the strong ellipticity, Hadamard and Coleman-Noll (GCN-condition) inequalities for nonlinear elastic shells. It is shown that the GCN-condition implies the strong elipticity for shell theory whereas the strong ellipticity is equivalent to the existence conditions of acceleration waves in shell. [ABSTRACT FROM AUTHOR]

The non-linear theory of elastic shells undergoing phase transitions was proposed by two first authors in J. Elast. 79, 67–86 (2004). In the present paper the theory is extended by taking into account also the elastic strain energy density of the curvilinear phase interface as well as the resultant forces and couples acting along the interface surface curve itself. All shell relations are found from the variational principle of stationary total potential energy. In particular, we derive the extended natural continuity conditions at coherent and/or incoherent surface curves modelling the phase interface. The continuity conditions allow one to establish the final position of the interface surface curve after the phase transition. The results are illustrated by an example of a phase transition in an infinite plate with a central hole. [ABSTRACT FROM AUTHOR]

The authors reflect on the modelling phase transitions (PT) in deformable solids. They mention that PT in deformable solids is one of the significant problems of continuum mechanics, mechanics of materials, and physics of solids due to the fact that materials in modern engineering went on PT during manufacturing. They also state that PT are the ancestry of mechanisms of shape memory effect and pseudoelasticity also known as superelasticity of shape memory of polymers and alloys.

Rotating micromachined beams are one of the most practical devices with several applications from power generation to aerospace industries. Moreover, recent advances in micromachining technology have led to huge interests in fabricating miniature turbines, gyroscopes and microsensors thanks to their high quality/reliability performances. To this end, this article is organized to examine the axial dynamic reaction of a rotating thermoelastic nanobeam under a constant‐velocity moving load. Using Eringen's nonlocal elasticity in conjunction with Euler–Bernoulli theory and Hamilton's principle, the governing equations are derived. It is assumed that the nanobeam is affected by thermal load and the boundary condition is simply supported. The Laplace transform approach is employed to solve the partial differential equations. A numerical example is presented to analyze the effects of the nonlocal parameter, rotation speed and velocity of the static moving load on the dynamic behavior of the system. The numerical results are graphically illustrated and analyzed to recognize the variations of field variables. Finally, in some special cases, our results are compared to those reported in the literature to demonstrate the reliability of the current model. [ABSTRACT FROM AUTHOR]