Quality Analysis of Nonlinear Elasticity Theory for the Stability Problems of Planar Laminated Curved Beams. Problem Statement

V. N. Paimushin; I. Sh. Gunal; S. A. Lukankin; V. A. Firsov

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Quality Analysis of Nonlinear Elasticity Theory for the Stability Problems of Planar Laminated Curved Beams. Problem Statement

机译：平面层合弯曲梁稳定性问题的非线性弹性理论质量分析。问题陈述

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The one-dimensional equations that describe the geometrically nonlinear deformation with arbitrary displacements and small strains are constructed for the planar laminated curved beams based on the Timoshenko model taking into account transverse compression. The equations are based on the relations of the classical nonlinear theory of elasticity for the case of realizing plane stressed state in a beam and also on the similar relations previously proposed in the consistent variant. Based on the equations constructed, we form the linearized equations of the neutral equilibrium of beams that enables investigating all possible buckling modes under the action of conservative forces and a stationary temperature field.

机译：基于Timoshenko模型，考虑了横向压缩，为平面叠层弯曲梁构造了描述任意位移和小应变的几何非线性变形的一维方程。对于在梁中实现平面应力状态的情况，这些方程式基于经典的非线性弹性理论的关系，并且还基于先前在一致变体中提出的相似关系。基于构造的方程式，我们形成了梁的中性平衡的线性化方程式，使我们能够研究在保守力和固定温度场作用下所有可能的屈曲模式。

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《Russian Aeronautics》 |2010年第2期|共6页
作者
V. N. Paimushin; I. Sh. Gunal; S. A. Lukankin; V. A. Firsov;
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正文语种 eng
中图分类航空;
关键词
Geometrical nonlinearity; Arbitrary displacements; Small strains; Plane stress state; Planar curved beam; Laminated structure; Timoshenko model; Neutral equilibrium equations;

机译：几何非线性;任意位移;小应变;平面应力状态;平面弯曲梁;叠层结构;Timoshenko模型;中性平衡方程;

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1. Quality Analysis of Nonlinear Elasticity Theory for the Stability Problems of Planar Laminated Curved Beams. Problem Statement [J] . V. N. Paimushin, I. Sh. Gunal, S. A. Lukankin, Russian Aeronautics . 2010,第2期

机译：平面层合弯曲梁稳定性问题的非线性弹性理论质量分析。问题陈述
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3. Wave propagation analysis in nonlinear curved single-walled carbon nanotubes based on nonlocal elasticity theory [J] . Wang Bo, Deng Zichen, Ouyang Huajiang, Physica, E. Low-dimensional systems & nanostructures . 2015,第Null期

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4. ANALYSIS OF THICK LAMINATED PANEL WITH PIEZOELECTRIC SENSORS BASED ON THREE-DIMENSIONAL THEORY OF ELASTICITY [C] . Daneshmehr A. R., Shakeri M., Alibiglu A. International Congress of Theoretical and Applied Mechanics . 2004

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5. Nonlinear instability and reliability analysis of composite laminated beams. [D] . Fereidooni, Alireza. 2009

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6. Piecewise affine stress-free martensitic inclusions in planar nonlinear elasticity [O] . S. Conti, M. Klar, B. Zwicknagl -1

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7. Nonlinear Analysis of Composite Laminates Using a Generalized Laminated Plate Theory [O] . E. J. Barbero, J. N. Reddyt 2010

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8. Analysis of Particulate Composite Behavior Based on Nonlinear Elasticity and an Improved Mori-Tanaka Theory. [R] . Wong, F. C. 1998

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Quality Analysis of Nonlinear Elasticity Theory for the Stability Problems of Planar Laminated Curved Beams. Problem Statement

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