Рівняння теорії пружності для композитних брусів із плоскою віссю довільної форми у природній криволінійній системі координат

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Ковальчук, Станіслав Богданович
Горик, Олексій Володимирович
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Луцький національний технічний університет
The work deals with the general dependences between the components of the stress-strain state for the composite discrete-inhomogeneous bar with a curvilinear plane axle of an arbitrary shape and the length-unchanged structural construction, that is subject to static, dynamic and temperature loads during the elastic behavior of orthotropic phase materials. To describe the geometry and the structural construction of the inhomogeneous bar it is proposed the use of natural curvilinear cylindrical coordinate system, which is tied to the shape of its axle, that allowed to reduce the number of variables in the functions of elastic characteristics and external load. The dependences between the components of the stress-strain state are constructed on the basis of the equations of the linear theory of elasticity in a rectangular spatial coordinate system by their coordinate transformation to the natural coordinate system. This made it possible to obtain relations invariant with respect to the shape of the bar, which can be used to solve a wide range of problems in mechanics of elastic deformation of structural elements of arbitrary curvature.
криволінійний брус, композит, природна система координат, напруження, деформації, переміщення, curvilinear bar, composite, natural coordinate system, stresses, strains, displacement, криволинейный брус, композит, естественная система координат, напряжения, деформации, перемещения