Construction of elastic fields for anisotropic bodies under the action of a local load
UDC
539.3DOI:
https://doi.org/10.31429/vestnik-21-4-29-37Abstract
The paper presents a mathematical model for constructing elastic non-axisymmetric fields for an anisotropic body bounded by coaxial surfaces of revolution. The body is in equilibrium under the action of external forces distributed over the body surface in a non-trivial manner. The cylinder material has rectilinear transverse isotropy. The model is constructed based on the energy method of boundary states. The basis of the space of internal states as part of the boundary state method is formed according to the general idea expressing the spatial stress-strain state through a set of plane auxiliary states. Such states are solutions to the problem of plane deformation. After forming the basis of internal states, it is orthogonalized, and the sought characteristics of the stress-strain state are expanded in a Fourier series by the elements of the orthonormal basis, where the coefficients are quadratures. The solution of the first main problem of elasticity theory for a circular cylinder made of transversely isotropic rock is presented. Surface forces are distributed over a complex function. The result is presented in graphical form.
Keywords:
boundary state method, transversely isotropic materials, spatial problem, asymmetric problemFunding information
The study did not have sponsorship.
References
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