Elastic equilibrium of an inhomogeneous orthotropic parallelepiped

Kolchin, G. B.; Plachinta, V. N.

doi:10.1007/bf01097438

Cited by 2 publications

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“…where the functions f a, b ð Þ n y ð Þ are orthonormal polynomials (9), satisfying conditions (6). Thus, the solution (10) exactly satisfies all boundary conditions on the plate contour.…”

Section: Problem Statement and Solution Methodsmentioning

confidence: 98%

“…Therefore, the expression (5) for the deflection W x, y ð Þ directly satisfies all the boundary conditions on the clamped edges but dont satisfy the differential equation ( 4). Now we define a system of polynomials f k y ð Þ that satisfy the conditions (6). These polynomials are constructed on the basis of Jacobi polynomials as follows.…”

Section: Problem Statement and Solution Methodsmentioning

confidence: 99%

“…which satisfy the conditions (6). The use of orthogonal polynomials satisfying homogeneous boundary conditions turns out to be effective in solving boundary value problems in the theory of thin plates with homogeneous boundary conditions by the classical Bubnov-Galerkin method.…”

Section: Problem Statement and Solution Methodsmentioning

confidence: 99%

“…In the article [6], the 3D problem of the theory of elasticity of an inhomogeneous body for an orthotropic rectangular region of finite dimensions with a free lateral surface is considered. The principle of minimum additional energy and the apparatus of special Horvey orthonormal polynomials are used.…”

Section: Introductionmentioning

confidence: 99%

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Bending of clamped orthotropic thin plates: polynomial solution

Goloskokov

Matrosov

2022

Mathematics and Mechanics of Solids

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In this paper, we study the bending of a clamped thin orthotropic plate by the Bubnov–Galerkin method. Special-type polynomials constructed on the basis of classical Jacobi polynomials and satisfying the clamped conditions are used as basis functions. The “quasi-orthogonality” property of first and second derivatives of the polynomials allows us to immediately write out the formula for the deflection of the plate in the form of a series, by analogy with the Navier method for a free-supported isotropic plate. This solution approximates well the displacement of the plate, but the series for moments and shear forces do not give reliable results. The refusal of using the “quasi-orthogonality” property of the polynomials leads to the solution of an infinite system of linear algebraic equations for finding unknown coefficients of series. The resulting series give reliable results for both displacements and moments and shear forces. The convergence of the series for displacement is very good, but it worsens for shearing forces and bending moments.

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Section: Problem Statement and Solution Methodsmentioning

confidence: 98%

Section: Problem Statement and Solution Methodsmentioning

confidence: 99%

Section: Problem Statement and Solution Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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