三维和四维弹性理论中的广义Cesaro公式

IF 0.9 4区工程技术 Q4 MECHANICS

Mechanics of Solids Pub Date : 2025-07-20 DOI:10.1134/S0025654425600436

S. A. Lurie, P. A. Belov

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引用次数: 0

摘要

建立了广义的Cesaro公式，利用三维弹性理论和四维弹性理论中的应变张量-偏差量的积分-微分算子，可以以高达二次多项式的精度确定位移场。结果表明，局部旋转和体积变化的伪向量（四维弹性中的伪张量）的正交是由应变偏差场决定的，其精度在坐标上可达线性多项式。所列正交存在的条件以关于应变张量偏差分量的5个（4D为9个）三阶相容方程的形式给出。

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Generalized Cesaro Formulas in 3D and 4D Elasticity Theories

Generalized Cesaro formulas are found, allowing to determine the displacement field with an accuracy of up to quadratic polynomials through integro-differential operators from the strain tensor-deviator in 3D elasticity theory and 4D elasticity theory. It is shown that quadratures for the pseudovector (pseudotensor in 4D elasticity) of local rotations and deformation of volume change are determined by the strain deviator field with an accuracy of up to linear polynomials in coordinates. Conditions for the existence of the listed quadratures are presented in the form of five (nine for 4D) third-differential order compatibility equations with respect to the strain tensor-deviator components.

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来源期刊

Mechanics of Solids 医学-力学

CiteScore

1.20

自引率

42.90%

发文量

112

审稿时长

6-12 weeks

期刊介绍： Mechanics of Solids publishes articles in the general areas of dynamics of particles and rigid bodies and the mechanics of deformable solids. The journal has a goal of being a comprehensive record of up-to-the-minute research results. The journal coverage is vibration of discrete and continuous systems; stability and optimization of mechanical systems; automatic control theory; dynamics of multiple body systems; elasticity, viscoelasticity and plasticity; mechanics of composite materials; theory of structures and structural stability; wave propagation and impact of solids; fracture mechanics; micromechanics of solids; mechanics of granular and geological materials; structure-fluid interaction; mechanical behavior of materials; gyroscopes and navigation systems; and nanomechanics. Most of the articles in the journal are theoretical and analytical. They present a blend of basic mechanics theory with analysis of contemporary technological problems.