The paper deals with the analysis of generalized von Kármán equations which describe stability of a thin circular clamped viscoelastic plate of constant thickness under a uniform compressive load which is applied along its edge and depends on a real parameter, and gives results for the linearized problem of stability of viscoelastic plates. An exact definition of a bifurcation point for the generalized von Kármán equations is given. Then relations between the critical points of the linearized problem...

The formulation of differential equations of buckling problem of anisotropic cylindrical shell is presented here. The solution for anisotropic cylindrical shells without shear load in case of two way compression is found out from the differential equations formulated. The corresponding results for isotropic case are deduced as a particular case.

The object of this paper is to find the solution of the differential equation of the buckling problem of anisotropic cylindrical shells with shear load in case of torsion of a long tube. The critical values of the shear load and the total torque are also found. The corresponding results for the isotropic case are deduced as a special case.

The object of this paper is to formulate the differential equations in the beamcolumn problem of the buckling of anisotropic cylindrical shells, placed between the plates of a testing machine subject to an axial load $P$ and a radial load $H$ of sufficient magnitude to bring the expansion without constraint of the edges produced by $P$ to zero deflection. The solution is obtained with necessary boundary conditions and the corresponding results for the isotropic case are deduced.

In this work we consider a solid body $\Omega \subset {ℝ}^3$ constituted by a nonhomogeneous elastoplastic material, submitted to a density of body forces $\lambda f$ and a density of forces $\lambda g$ acting on the boundary where the real $\lambda$ is the loading parameter. The problem is to determine, in the case of an unbounded convex of elasticity, the Limit load denoted by $\overline{\lambda }$ beyond which there is a break of the structure. The case of a bounded convex of elasticity is done in [El-Fekih and Hadhri, RAIRO: Modél. Math. Anal. Numér. 29 (1995)...

In this work we consider a solid body $\Omega \subset {ℝ}^3$ constituted by a nonhomogeneous elastoplastic material, submitted to a density of body forces $\lambda f$ and a density of forces $\lambda g$ acting on the boundary where the real $\lambda$ is the loading parameter. The problem is to determine, in the case of an unbounded convex of elasticity, the Limit load denoted by $\overline{\lambda }$ beyond which there is a break of the structure. The case of a bounded convex of elasticity is done in [El-Fekih and Hadhri, RAIRO: Modél. Math. Anal. Numér. 29 (1995)...

We investigate collisions (assumed to be instantaneous) and fractures of three-dimensional solids. Equations of motion and constitutive laws provide a set of partial differential equations, whose corresponding variational problem may be solved in the space of special functions with bounded deformations ($SBD$), exploiting the direct method of calculus of variations.

This paper is concerned with the computation of 3D vertex singularities of anisotropic elastic fields with Dirichlet boundary conditions, focusing on the derivation of error estimates for a finite element method on graded meshes. The singularities are described by eigenpairs of a corresponding operator pencil on spherical polygonal domains. The main idea is to introduce a modified quadratic variational boundary eigenvalue problem which consists of two self-adjoint, positive definite sesquilinear...

This paper is concerned with the computation of 3D vertex singularities of anisotropic elastic fields with Dirichlet boundary conditions, focusing on the derivation of error estimates for a finite element method on graded meshes. The singularities are described by eigenpairs of a corresponding operator pencil on spherical polygonal domains. The main idea is to introduce a modified quadratic variational boundary eigenvalue problem which consists of two self-adjoint, positive definite sesquilinear...

We consider coupled structures consisting of two different linear elastic materials bonded along an interface. The material discontinuities combined with geometrical peculiarities of the outer boundary lead to unbounded stresses. The mathematical analysis of the singular behaviour of the elastic fields, especially near points where the interface meets the outer boundary, can be performed by means of asymptotic expansions with respect to the distance from the geometrical and structural singularities....

In this paper we present a few results on convergence for the prime integrals equations connected with the bounce problem. This approach allows both to prove uniqueness for the one-dimensional bounce problem for almost all permissible Cauchy data (see also [6]) and to deepen previous results (see [3], [5], [7]).

Let $F^{\mathrm{p}}\in \mathrm{GL}\left(3\right)$ be the plastic deformation from the multiplicative decomposition in elasto-plasticity. We show that the geometric dislocation density tensor of Gurtin in the form $\mathrm{Curl}\left[F^{\mathrm{p}}\right]·{\left(F^{\mathrm{p}}\right)}^T$ applied to rotations controls the gradient in the sense that pointwise $\forall R\in C^1({ℝ}^3,\mathrm{SO}\left(3\right)):\parallel \mathrm{Curl}\left[R\right]·R^T{\parallel }_{{𝕄}^{3\times 3}}^2\ge \frac{1}{2}{\parallel \mathrm{D}R\parallel }_{{ℝ}^{27}}^2$. This result complements rigidity results [Friesecke, James and Müller, Comme Pure Appl. Math. 55 (2002) 1461–1506; John, Comme Pure Appl. Math. 14 (1961) 391–413; Reshetnyak, Siberian Math. J. 8 (1967) 631–653)] as well as an associated linearized theorem...

Let $F^{\mathrm{p}}\in \mathrm{GL}\left(3\right)$ be the plastic deformation from the multiplicative decomposition in elasto-plasticity. We show that the geometric dislocation density tensor of Gurtin in the form $\mathrm{Curl}\left[F^{\mathrm{p}}\right]·{\left(F^{\mathrm{p}}\right)}^T$ applied to rotations controls the gradient in the sense that pointwise $\forall R\in C^1({ℝ}^3,\mathrm{SO}\left(3\right)):\parallel \mathrm{Curl}\left[R\right]·R^T{\parallel }_{{𝕄}^{3\times 3}}^2\ge \frac{1}{2}{\parallel \mathrm{D}R\parallel }_{{ℝ}^{27}}^2$. This result complements rigidity results [Friesecke, James and Müller, Comme Pure Appl. Math.55 (2002) 1461–1506; John, Comme Pure Appl. Math.14 (1961) 391–413; Reshetnyak, Siberian Math. J.8 (1967) 631–653)] as well as an associated linearized theorem saying...

Elastic two-layer curved composite beam with partial shear interaction is considered. It is assumed that each curved layer separately follows the Euler-Bernoulli hypothesis and the load slip relation for the flexible shear connection is a linear relationship. The curved composite beam at one of the end cross sections is fixed and the other end cross section is subjected by a concentrated radial load. Two cases are considered. In the first case the loaded end cross section is closed by a rigid plate...