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Problem of elasticity and plasticity for a plate with a shape of \(n\)-angle weakened by \(n\)-holes. (English) Zbl 1307.74047

Summary: We consider a homogeneous, isotropic plate with a shape of rectilinear \(n\)-angle weakened by \(n\)-cyclic symmetric holes. The plate is in a stressed state; a region of plasticity contains only contours of holes and does not spread inside of the plate. A problem of elasticity and plasticity for this plate is reduced to a boundary problem of linear relationship for a unit circle with sectionally constant coefficients. The equation of unknown contours of holes is presented; the solution of this problem is obtained.

MSC:

74K20 Plates
74B99 Elastic materials
74C99 Plastic materials, materials of stress-rate and internal-variable type
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