Figure - available from: Acta Mechanica
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Diagram of relevant angles and vectors
Source publication
In this article, we consider a variant of the Simo–Reissner theory for a rod but restrict the study to two-dimensional motion where the rod undergoes flexure, shear and extension but not torsion. Linear elastic behaviour is assumed to formulate constitutive equations; the constitutive equations of the Timoshenko theory adapted for extension and lar...
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Fuzzy linear programming has a wide range of applications in agricultural economic management. In this paper, the mathematical model of fuzzy linear programming was studied in detail, and then under the restriction of elastic constraints, the f(ti) and g (t0) function expressions and their optimal solutions were obtained. Subsequently, the fuzzy li...
Citations
The Local Linear Timoshenko (LLT) model for the planar motion of a rod that undergoes flexure, shear and extension, was recently derived in Van Rensburg et al. (2021). In this paper we present an algorithm developed for this model. The algorithm is based on the mixed finite element method, and projections into finite dimensional subspaces are used for dealing with nonlinear forces and moments. The algorithm is used for an investigation into elastic waves propagated in the LLT rod. Interesting properties of the LLT rod include the increased propagation speed of elastic waves when compared to the linear Timoshenko beam, and the appearance of buckled states or equilibrium solutions for compressed LLT beams. It is also shown that the LLT rod is applicable to large displacements and rotations for a wide range of slender elastic objects; from beams to highly slender flexible rods.
