In this work, we show that the eigenvalues of the problem  (∆2 + V (x) + λ)u(x) = 0 x ∈ Ω u(x) = ∆u(x) = 0 x ∈ ∂Ω are generically simple in the set of C4 regular regions of Rn, n ≥ 2. In fact, we prove that there exists a residual set of regions C4 diffeomorphic to a given Ω such that all the eigenvalues for a supported plate equation are simple.

The theory of contact mechanics deals with stresses and deformations which arise when the surfaces of two solid bodies are brought into contact. In elastic deformation contact occurs over a finite area. A regular method for determining the dimensions of this area is Hertz Contact Model. Appearance of atomic force microscope results in introduction of Contact ...

With the increasing complexity of photo-realistic scenes, the question of building and placing objects in three-dimensional scenes is becoming ever more di cult. While the question of placement of rigid objects has captured the attention of researchers in the past, this work presents an intuitive and interactive scheme to properly place deformable objects with the aid of free-form deformation t...

geometrically nonlinear governing equations for a plate with linear viscoelastic material are derived. the material model is of boltzmann superposi¬tion principle type. a third-order displacement field is used to model the shear deformation effects. for the solution of the nonlinear governing equations the dynamic relaxation (dr) iterative method together with the finite difference discretizati...

Given the set of square matrices M ⊂ Mn+m(C) that keep the subspace W = Cnx{0} ⊂ C invariant, we obtain the implicit form of a miniversal deformation of a matrix a ∈ M, and we compute it explicitely when this matrix is marked (this is, if there is a permutation matrix p ∈ Mn+m(C) such that p−1ap is a Jordan matrix). We derive some applications to tackle the classical Carlson problem.

2 Kinematics 12 2.1 Geometric interpretation of the deformation gradient . . . . . . . . . . . . . . . . . . 12 2.2 Small strain and linearization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.3 Transformations of a deformation gradient . . . . . . . . . . . . . . . . . . . . . . . . 14 2.4 Compatibility conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....

Non-geometric string backgrounds were proposed to be related to a nonassociative deformation of the space-time geometry. In the flux formulation of double field theory (DFT), the structure of mathematically possible non-associative deformations is analyzed in detail. It is argued that on-shell there should not be any violation of associativity in the effective DFT action. For imposing either th...

If little is known about the sample under test, ascertaining a quantitative material true stress–true strain relationship from a small punch test is not direct. Conventional inverse simulation methods have used experimental force–displacement curves that ignore the deformation shape of the punched sample. We present small punch test methodology and results that used experimental deformation sha...

We develop a thermodynamic model of electrostriction for elastic dielectrics capable of large deformation. The model reproduces the classical equations of state for dielectrics at small deformation, but shows that some electrostrictive effects negligible at small deformation may become pronounced at large deformation. The model is then specialized to account for recent experiments with an elast...