Membrane Theory of Plates

Ambartsumian,; Sergey, A

doi:10.1007/978-3-030-71326-3_4

Cited by 1 publication

(1 citation statement)

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“…The configuration of the plate is determined by three parameters: a this is the base of the triangle (plate); α, β are the angles of inclination of the side edges to the base (in the general case, α is not equal to β). The study used the well-known initial differential equation to bend orthotropic plates [24][25][26]. The equation has the form:…”

Section: Methodsmentioning

confidence: 99%

Bending of Orthotropic Scalene Triangle Plates: Finite Difference Modeling

Akhmediev,

Beketova,

Nuguzhinov

et al. 2023

Preprint

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The object of study is a transversely bent triangular plate made of orthotropic material fixed along the edges of the plate under the action of a uniformly distributed load. Fourth-order differential equilibrium equations with variable orthotropy parameters were used. The equations were approximated by finite differences for a grid of scalene triangles. This type of mesh accurately describes the boundary contour of the triangular-shaped plates. The boundary conditions for the mesh consider the orthotropy of the plate material. Seven standard finite-difference equations have been developed considering the boundary conditions along the three edges of the plate and the presence of three angles of an irregularly shaped triangle. A finite difference matrix is obtained. The matrix structure makes calculating a triangular plate at different base angles possible. The boundary conditions were varied in the form of rigid or hinged support of triangular plates. The calculation method considers the orthotropic parameters of the material in two mutually perpendicular planes. The adaptation of the numerical method to the calculation of orthotropic plates of arbitrary shape is described. Relationships are given for determining the rigidity characteristics of orthotropic materials. An algorithm for simple engineering calculation of triangular orthotropic plates is proposed, which makes it possible to perform accurate calculations in variant design.

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Section: Methodsmentioning

confidence: 99%