Numerical response using finite strip element including drilling degree of freedom

Finite-element modeling of structures using elements without rotational degrees of freedom (DOFs) is usually stiffer than their physical behavior. Therefore, the stiffness of a structural system will be smoothed by adding rotational DOFs in the numerical model. In the traditional displacement-based finite-element method, adding drilling rotations is not easy. The main contribution of this paper is performing dynamic analyses using the finite strip element with added drilling rotations to the elements. For this purpose, any quadrilateral area is divided into two independent sets of orthogonal strips comprising truss and Bernoulli-Euler beam elements. Then by using new shape functions, mass, damping, stiffness matrices, and equivalent nodal forces are derived. Finally, time history analysis for plane stress or strain type problems for direct earthquake records is performed using the developed formulations. The numerical studies show that the results of the finite strip method using coarse meshes are competitive with the results of the finite-element method using fine meshes. This advantage is valuable in time-consuming computational problems, e.g., dynamic or nonlinear analyses.