An Explicit Stiffness Matrix for Parabolic Beam Element

作者：Rezaiee Pajand Mohammad^*; Rajabzadeh Safaei Niloofar

来源：Latin American Journal of Solids and Structures, 2016, 13(9): 1782-1801.

DOI：10.1590/1679-78252820

• Finite element method
• parabolic beam
• explicit stiffness matrix
• strain-based formulation
• equilibrium conditions

This study is devoted to strain-based formulation for a curved beam. Arches with parabolic geometry, which have a variety of applications, belong to this structural type. Dependency of the curvature radius to the arch length creates some complexities in the solution process. To analyze these complex structures, a two-node beam with six degrees of freedom is suggested by utilizing closed-form solution and the stiffness-based finite element method. Considering the effect of shear deformation, and incorporating equilibrium conditions into the finite element model, lead to the exact strains. Displacements and explicit stiffness matrix are found based on these exact strains. To validate the efficiency of the author's formulation, seven numerical tests are performed. The outcomes demonstrate that by employing only a single element, the locking-free answers can be found.

• 出版日期2016