On 3D and 1D mathematical modeling of physically nonlinear beams

被引：8

作者：

Krysko, A., V ^{[1
]}

Awrejcewicz, J. ^{[2
]}

Zhigalov, M., V ^{[3
]}

Bodyagina, K. S. ^{[3
]}

Krysko, V. A. ^{[3
]}

机构：

[1] Saratov State Tech Univ, Sci & Educ Ctr, Dept Math & Modelling, Politehn Skaya 77, Saratov 410054, Russia

[2] Lodz Univ Technol, Dept Automat Biomech & Mechatron, 1-15 Stefanowskiego Str, PL-90924 Lodz, Poland

[3] Saratov State Tech Univ, Dept Math & Modelling, Politehn Skaya 77, Saratov 410054, Russia

来源：

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS | 2021年 / 134卷

基金：

俄罗斯基础研究基金会;

关键词：

Physical nonlinearity; 3D (1D) theory; Nonhomogeneous plates; Euler-Bernoulli model; Timoshenko model; Finite element method; Method of variable elasticity parameters; ELASTOPLASTIC TORSION; SHELLS; BEHAVIOR; BARS;

D O I：

10.1016/j.ijnonlinmec.2021.103734

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

In this work, mathematical models of physically nonlinear beams (and plates) are constructed in a three-dimensional and one-dimensional formulation based on the kinematic models of Euler-Bernoulli and Timoshenko. The modeling includes achievements of the deformation theory of plasticity, the von Mises plasticity criterion and the method of variable parameters of the Birger theory of elasticity. The theory is built for arbitrary boundary conditions, transverse loads, and stress-strain diagrams. The issue of solving perforated structures is also addressed. The numerical investigations are based on the finite element method and the method of variable elasticity parameters. Convergence of the method is also investigated.

引用

页数：18

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