A strip with constant stresses on the cut: Exact solutions. Issue 10 (22nd July 2022)

• Record Type: Journal Article
• Authors: Kovalenko, Mikhail D.; Menshova, Irina V.; Kerzhaev, Alexander P.; Yu, Guangming
• Is Part Of: Zeitschrift für angewandte Mathematik und Mechanik. Volume 102:Issue 10(2022)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2022-07-22
• Subjects: Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; Engineering -- Periodicals; 519
• DOI: 10.1002/zamm.202100431
• Languages: English
• ISSNs: 0044-2267

Abstract

Abstract: We construct exact solutions of three boundary value problems in the theory of elasticity for an infinite strip with a central transverse cut on which constant normal stresses are specified (even‐symmetric deformation). We consider three variants of homogeneous boundary conditions on the strip sides: (1) free sides, (2) firmly clamped sides, and (3) there are identical stiffeners on the strip sides. The solutions of all problems are represented as series in Papkovich–Fadle eigenfunctions whose coefficients are determined from simple closed formulas. Abstract : We construct exact solutions of three boundary value problems in the theory of elasticity for an infinite strip with a central transverse cut on which constant normal stresses are specified (even‐symmetric deformation). We consider three variants of homogeneous boundary conditions on the strip sides: (1) free sides, (2) firmly clamped sides, and (3) there are identical stiffeners on the strip sides. The solutions of all problems are represented as series in Papkovich–Fadle eigenfunctions whose coefficients are determined from simple closed formulas.