دانلود مقاله STIFFNESS MATRIX OF A NEW CRACKED BEAM FINITE ELEMENT USING THE CONJUGATED BEAM METHOD AND BETTI’S LAW
سال انتشار: ۱۳۹۰
محل انتشار: ششمین کنفرانس بین المللی زلزله شناسی و مهندسی زلزله
تعداد صفحات: ۸
m Mehrjoo – Department of Civil Engineering, Islamic Azad University Hamedan Branch, Hamedan, Iran
n Khaji – Faculty of Civil and Environmental Engineering, Tarbiat Modares University, Tehran, Iran
In this paper, the finite element of beam element with a transverse crack is derived for fatigue and fracture applications. The new element is one-dimensional with an embedded edge crack in arbitrary position of beam element with any depth. The crack is not physically modeled within the element, but instead, its effect on the local flexibility of the structure is considered by the modification of the element stiffness as a function of the crack depth and crack position. The derivations are based on a simplified computational model, where each crack is replaced by a corresponding linear rotational spring, connecting two adjacent elastic parts. The components of the stiffness matrix for the cracked element are determined from the Conjugated beam method and Betti’s law. The stiffness matrix for transversely cracked beam element is derived and all components are given in closed-form. Models using the presented stiffness matrix are shown to produce accurate results, with significantly less computational effort than numerical modeling of the crack in two-dimensional finite element models.