Extensions of the Castigliano theorems are developed in the context of modeling the behavior of both discrete coupled linear systems and various coupled beams. It is shown that the minimization of the displacement of a parallel system determined from Castigliano’s second theorem can be used to formally define the apportionment of loads among the system elements, while the minimization of the lo...

A thermomechanical model for shape memory alloy (SMA) actuators and SMA hybrid composite (SMAHC) structures has been recently implemented in the commercial finite element codes MSC.Nastran and ABAQUS. The model may be easily implemented in any code that has the capability for analysis of laminated composite structures with temperature dependent material properties. The model is also relatively ...

In this paper, based on Kelvin and Linear Standard Solid models, dynamic response and the buckling load of a viscoelastic beam under  lateral and axial loads have been determined. The governing equations have been extracted using Euler  and Timoshenko theories and their analytical solutions have been obtained by using the eigenfunctions expansion method. Buckling load have been calculated by us...

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 ana...

In this paper, surface and piezoelectric effects on the vibration behavior of nanowires (NWs) are investigated by using a Timoshenko beam model. The electric field equations and the governing equations of motion for the piezoelectric NWs are derived with the consideration of surface effects. By the exact solution of the governing equations, an expression for the natural frequencies of NWs with ...

Modified couple stress theory is applied to study of temperature effects on free vibration of Timoshenko functionally graded microbeams. Due to the interatomic and microstructural reactions of the structures in micro scale, the dynamic behavior of the microbeam is predicted more accurate applying the couple stress theory. Both of the simply supported and clamped boundary conditions are assumed ...