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Analysis of thin-walled beams with variable monosymmetric cross section by means of Legendre polynomials

versors of the cartesian coordinate system basis. The vectors of the covariant basis of the system of coordinates (t, s, n), determined on the central surface of the shell are defined as follows: (2) a t = e x + y , t e y + z , t e z , a s = y , s e y + z , s e z , $${{a}_{t}}={{e}_{x}}+{{y}_{,t}}{{e}_{y}}+{{z}_{,t}}{{e}_{z}},{{a}_{s}}={{y}_{,s}}{{e}_{y}}+{{z}_{,s}}{{e}_{z}},$$ where f , s = ∂ f ( t ,   s ) / ∂ s     , f , t = ∂ f ( t ,   s ) / ∂ t   . $${{f}_{,s}}=\partial f\left( t,\,s \right)\text{/}\partial s\,\,,{{f}_{,t}}=\partial f

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