Mathematical modeling of planar physically nonlinear inhomogeneous plates with rectangular cuts in the three-dimensional formulation

• Published in: Acta mechanica Vol. 232; no. 12; pp. 4933 - 4950
• Main Authors: Krysko, A. V., Awrejcewicz, J., Bodyagina, K. S., Krysko, V. A.
• Format: Journal Article
• Language: English
• Published: Vienna Springer Vienna 01.12.2021; Springer; Springer Nature B.V
• Subjects: Boundary conditions; Classical and Continuum Physics; Control; Deformation; Dynamical Systems; Engineering; Engineering Fluid Dynamics; Engineering Thermodynamics; Finite element analysis; Finite element method; Geometry; Heat and Mass Transfer; Inhomogeneity; Investigations; Mathematical models; Original Paper; Plastic deformation; Plates; Solid Mechanics; Strain; Stress analysis; Stress concentration; Theoretical and Applied Mechanics; Three dimensional models; Transverse loads; Vibration
• ISSN: 0001-5970; 1619-6937
• DOI: 10.1007/s00707-021-03096-0

Mathematical models of planar physically nonlinear inhomogeneous plates with rectangular cuts are constructed based on the three-dimensional (3D) theory of elasticity, the Mises plasticity criterion, and Birger’s method of variable parameters. The theory is developed for arbitrary deformation diagrams, boundary conditions, transverse loads, and material inhomogeneities. Additionally, inhomogeneities in the form of holes of any size and shape are considered. The finite element method is employed to solve the problem, and the convergence of this method is examined. Finally, based on numerical experiments, the influence of various inhomogeneities in the plates on their stress–strain states under the action of static mechanical loads is presented and discussed. Results show that these imbalances existing with the plate’s structure lead to increased plastic deformation.