Vibration and static analysis of cracked and non-cracked non-prismatic frames by force formulation. (15th April 2019) - Rezaiee-Pajand, Mohammad; Gharaei-Moghaddam, Nima
Highlights: A new force-based non-prismatic frame element containing open stable edge cracks is proposed. Due to utilization of the force method, the suggested element is locking free. A consistent mass matrix is developed and the validity of using non-cracked mass matrix for the crack element is verified numerically. The effect of the crack interference on the accuracy of the proposed element is investigated by a case study problem. Application of compliance concept for including crack effect removes the necessity of remeshing in vibration-based crack detection. Abstract: Consistent mass and stiffness matrices are formulated for a new frame element. It is assumed that the frame member contains stable open edge cracks. All axial, bending, and shear effects are included in this study. Moreover, the proposed element has a non-prismatic property. Flexibility matrix of this structure consists of two parts. The first part is the flexibility of the non-cracked element, which is formulated in a basic coordinate system without rigid body motions. The additional flexibility due to cracks is the second part, which is calculated by using the fracture mechanics principles. The proposed element is applicable for both frame vibration and static analyses. It is a widely accepted assumption that cracking does not affect the distribution of the inertia components. In other words, mass matrices of the cracked and non-cracked elements are the same. Accuracy of this assumption is also reinvestigated in this study by using the developed consistent mass matrix. Various numerical examples are used to evaluate accuracy and capabilities of the novel element. Due to force method, the present formulation is locking free.