Variational and Potential Methods in the Theory of Bending of Plates with Transverse Shear Deformation

Weak solutions of the transmission problem in anti‐plane Cosserat elasticity

“…,ω (S − ) and according to (42) a i+ (u + , w + − v + ) = 0 and a i− (u − , w − − v − ) = 0. Let us recall the properties of Poincaré-Steklov operators, discussed in details in [23].…”

“…Chudinovich and Constanda in [23] suggested that the boundary value problems arising in the bending of plates be formulated in a weak (Sobolev) space setting. Later this approach was successfully used for various problems of plane and anti-plane Cosserat elasticity, [24][25][26][27].…”

Variational Formulation of Crack Problems in Three-dimensional Classical Elasticity

“…Let S 6 be a domain bounded by a closed C 2 -surface 7 S, S 8 3 R 3 4S 6 7 S5.…”

“…In spite of the fact that the methods used are extremely complicated (mathematically) they seem to be very effective and give very good results for applications. In [9][10][11] the results obtained in [8] have been extended to the investigation of boundary value problems for cracks in micropolar media by Shmoylova and Potapenko. In this paper, using the results obtained in [9][10][11], we formulate the boundary value problems for infinite domain which contains a crack in the case of three-dimensional elasticity when displacements or stresses are prescribed along the two sides of the crack in Sobolev spaces, show well-posedness and solvability of these problems and prove the uniqueness theorems.…”

“…Recently, Chudinovich and Constanda [8] have used the boundary integral equation method in a weak (Sobolev) space setting to obtain the solution for several crack problems VARIATIONAL FORMULATION OF CRACK PROBLEMS 871 in a theory of bending of classical elastic plates. In spite of the fact that the methods used are extremely complicated (mathematically) they seem to be very effective and give very good results for applications.…”