Analysis of Timoshenko–Ehrenfest beam problems using the Theory of Functional Connections

The numerical solution of boundary value problems in solid mechanics is dominated by the Finite Element Method (FEM). present study provides an alternative approach using Theory Functional Connections (TFC) for solving this type. Here TFC used to solve multiple beam Timoshenko–Ehrenfest theory which accounts transverse shear strain. results obtained are then compared those with both FEM and analytical approaches. For cases where continuous smooth, out performs terms L2 norm residuals time. When on order machine-error level precision. However, when higher derivatives discontinuous (i.e. applied load discontinuous), under FEM. This due approximating functions true piece-wise continuous. In computational expense, consistently solved differential equations faster than across each type problem analyzed paper.