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The saint-venant torsion of a cartesian orthotropic bar with an isosceles right-angled triangle cross-section

Ecsedi István, Baksa Attila

Engineering Transactions

2024

Vol. 72, iss. 1

81--94

The Saint-Venant torsion of the Cartesian orthotropic homogeneous linearly elastic bar is considered. The cross-section of the prismatic bar is an isosceles right-angled triangular plane domain. An approximate analytical method is presented to obtain Prandtl’s stress function, shearing stresses, and torsional rigidity. Upper and lower bounds for the torsional rigidity are provided. The obtained results for shearing stresses are verified through FEM computation.

A new modification of the reduced differential transform method for nonlinear fractional partial differential equations

Khalouta Ali, Kadem Abdelouahab

Journal of Applied Mathematics and Computational Mechanics

2020

Vol. 19, nr 3

45--58

The objective of this study is to present a new modification of the reduced differential transform method (MRDTM) to find an approximate analytical solution of a certain class of nonlinear fractional partial differential equations in particular, nonlinear time-fractional wave-like equations with variable coefficients. This method is a combination of two different methods: the Shehu transform method and the reduced differential transform method. The advantage of the MRDTM is to find the solution without discretization, linearization or restrictive assumptions. Three different examples are presented to demonstrate the applicability and effectiveness of the MRDTM. The numerical results show that the proposed modification is very effective and simple for solving nonlinear fractional partial differential equations.

Transient Space-fractional Diffusion with a Power-law Superdiffusivity : Approximate Integral-balance Approach

Hristov J.

Fundamenta Informaticae

2017

Vol. 151, nr 1/4

371--388

This paper focuses on an approximate analytical solution of an initial-boundary value problem of spatial-fractional partial differential diffusion equation with RiemannLiouville fractional derivative in space. The spatial correlation of the superdiffusion coefficient as a power-law has been discussed in cases of fast and slow spatial superdiffusion. Approximate closed form solutions in terms of non-linear similarity variable are based on the integral-balance method and series expansion of the assumed parabolic profile with undefined exponent. The law of the spatial and temporal propagation of the solution was the primary issue and discussed in two cases: fast and slow superdiffussion.