TY - JOUR

T1 - Modeling Nonlinear Deformation of a Plate with an Elliptic Inclusion by John's Harmonic Material

AU - Mal’kov, V. M.

AU - Mal’kova, Yu. V.

N1 - Mal’kov, V.M., Mal’kova, Y.V. Modeling nonlinear deformation of a plate with an elliptic inclusion by John’s harmonic material. Vestnik St.Petersb. Univ.Math. 50, 74–81 (2017). https://doi.org/10.3103/S1063454117010095

PY - 2017/4/19

Y1 - 2017/4/19

N2 - The exact analytical solution of a nonlinear plane-strain problem has been obtained for a plate with an elastic elliptic inclusion with constant stresses given at infinity. The mechanical properties of the plate and inclusion are described with the model of John’s harmonic material. In this model, stresses and displacements are expressed in terms of two analytical functions of a complex variable that are determined from nonlinear boundary-value problems. Assuming the tensor of nominal stresses to be constant inside the inclusion has made it possible to reduce the problem to solving two simpler problems for a plate with an elliptic hole. The validity of the adopted hypothesis has been justified by the fact that the derived solution exactly satisfies all the equations and boundary conditions of the problem. The existence of critical plate-compression loads that lead to the loss of stability of the material has been established. Two special nonlinear problems for a plate with a free elliptic hole and a plate with a rigid inclusion have been solved.

AB - The exact analytical solution of a nonlinear plane-strain problem has been obtained for a plate with an elastic elliptic inclusion with constant stresses given at infinity. The mechanical properties of the plate and inclusion are described with the model of John’s harmonic material. In this model, stresses and displacements are expressed in terms of two analytical functions of a complex variable that are determined from nonlinear boundary-value problems. Assuming the tensor of nominal stresses to be constant inside the inclusion has made it possible to reduce the problem to solving two simpler problems for a plate with an elliptic hole. The validity of the adopted hypothesis has been justified by the fact that the derived solution exactly satisfies all the equations and boundary conditions of the problem. The existence of critical plate-compression loads that lead to the loss of stability of the material has been established. Two special nonlinear problems for a plate with a free elliptic hole and a plate with a rigid inclusion have been solved.

KW - nonlinear plane problem

KW - elliptic inclusion (hole)

KW - John’s harmonic material

KW - complex function method

UR - https://link.springer.com/article/10.3103/S1063454117010095

M3 - Article

VL - 50

SP - 74

EP - 81

JO - Vestnik St. Petersburg University: Mathematics

JF - Vestnik St. Petersburg University: Mathematics

SN - 1063-4541

IS - 1

ER -