development of a new analytical method to calculate the static deflection of a truss like structure with repeated cells

Failure of telecommunication towers due to static loading of wind causes many accidents every year. having a close form solution to calculate the deflection of a complicated structure is necessary in many applications such as optimization, control loops or failure prediction. the static deflection of 2d truss -for a certain application in a machine- has been extracted in this study. the method is based on continuum modeling methods. unlike previous works in the literature the displacement field of timoshenko has been used to model the structure as a continuum. in this method the work of external loads and strain energy of the representative cell is calculated as the first step. on the next step the functionals are extracted from which the governing equations are obtained. the last step includes applying the boundary conditions and solving the equations. the answers are applicable in case of linear modeling. because the displacement field is considered to be linear. as the geometry is straight forward and the fem is proved to get precise results in this type of problems, fem has been used to evaluate the method.