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.

Thermal residual stresses exist within a body in the absence of external loading or thermal gradients. Processing of the composites often involves cooling from higher temperature resulting in thermal residual stresses in the matrix due to restraint imposed by reinforcements. Thermal residual stresses determinately affect the properties of materials thereby shortening their lifetime. These resid...

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...

The paper includes the second part of an investigation of the braking process of railway vehicles, dealing with the temperature distribution of a brake block in various load cases and the FE analysis of the phenomenon of thermal elastic deformation. Thermal expansion calculations pointed out to the fact that in case of the contact area, the radius of the operating surface of the brake block inc...

The thermal stability of the machining centers plays a major role in ensuring production repeatability. All machine tools producers take various steps to ensure it. One ways permanently maintain and stabilize behavior tool is use active cooling choice appropriate material which individual parts supporting system are made. In most cases, manufacturers traditional metallic materials (steel, cast ...

A functionally graded material beam with generalized boundary conditions is contemplated in the present study in order to examine the deformation and stress behavior under thermal and thermo-mechanical load. Three discrete combinations of functionally graded materials have been deliberate in including a wide range of materials and material properties. The variation of material properties has be...

Potential problems induced by the multilayered manufacturing process pose a serious threat to the long-term reliability of MEMSCAP® actuators under in-service thermal cycling. Damage would initiate and propagate in different material layers because of a large mismatch of their thermal expansions. In this research, residual stresses and variations of design parameters induced by metal multi-user...

In the process of heavy oil thermal recovery, the creep of strata can often be accelerated due to injection pressure, the temperature of steam, the structural characteristics of rock itself and other factors. However, the effect of creep in strata may cause various types of damage in underground mining, such as fracture or deformation of oil casings, and so on. The mechanism of fluid–structure ...