The key point in this paper is the introduction of elastic analytic functions. An elastic analytic function is a function of the form u : C ! C 2 which is diierentiable and satisses equations which are analogous to the Cauchy-Riemann equations of traditional complex analysis such that the following conditions hold: rst the real and imaginary part of the rst complex component of u satisfy the Na...

The Dirichlet problem for the plane elasticity problem on a convex polygonal domain is considered and it is proved that for data in L the H regularity estimate holds with constants independent of the Lamé coefficients.

The Dirichlet problem for the plane elasticity problem on a convex polygonal domain is considered and it is proved that for data in L the H regularity estimate holds with constants independent of the Lamé coefficients.

Nowadays, functionally graded materials (FGM) are widely used in many industrial, aerospace and military fields. On the other hand, the interest in the use of shrink-fitted assemblies is increasing for designing composite tubes, high-pressure vessels, rectors and tanks. Although extensive researches exist on thick-walled cylindrical shells, not many researches have been done on shrink-fitted th...

This paper proposed analytical solutions for the buckling analysis of rectangular single-layered graphene sheets under in-plane loading on all edges simply is supported. The characteristic equations of the graphene sheets are derived and the analysis formula is based on the nonlocal Mindlin plate. This theory is considering both the small length scale effects and transverse shear deformation ef...

This paper proposed analytical solutions for the buckling analysis of rectangular single-layered graphene sheets under in-plane loading on all edges simply is supported. The characteristic equations of the graphene sheets are derived and the analysis formula is based on the nonlocal Mindlin plate. This theory is considering both the small length scale effects and transverse shear deformation ef...

We prove the strong unique continuation property for the Lamé system of elastostatics in the plane, ∇· ( μ ( ∇u+∇ut )) +∇ (λ∇ · u) = 0, with variable Lamé coefficients μ, λ, when μ is Lipschitz and λ is measurable.

Recently a stable pair of finite element spaces for the mixed formulation of the plane elasticity system has been developed by Arnold and Winther. Here we construct a two-level overlapping Schwarz preconditioner for the resulting discrete system. Essentially, this reduces to finding an efficient preconditioner for the form (·, ·) + (div ·,div ·) in the symmetric tensor space H(div ,Ω). The main...

algorithm: variable V-cycle Let mk be the number of smoothings and assume that β0mk ≤ mk−1 ≤ β1mk , where 1 < β0 ≤ β1. Algorithm Let B1 = Λ −1 1 . Assuming Bk−1 : Σk−1 → Σk−1 be defined, define Bk : Σk → Σk as follows. Let g ∈ Σk and τ 0 = 0. (1) τ l = τ l−1 + Rk(g −Λkτ ) for l = 1, · · · , mk; (2) σk = τk + IkBk−1I t k(g −Λkτ k); (3) σ = σ + Rk(g −Λkσ ) for l = mk + 1, · · · , 2mk ; Set Bkg = ...