A Three dimensional mixed formulation nonlinear frame finite element based on hu-washizu functional

Soydaş, Ozan
A three dimensional nonlinear frame finite element is presented in this analytical study by utilizing Hu-Washizu principle with three fields of displacement, strain and stress in the variational form. Timoshenko beam theory is extended to three dimensions in order to derive strains from the displacement field. The finite element approximation for the beam uses shape functions for section forces that satisfy equilibrium and discontinous section deformations along the beam. Nonlinear analyses are performed by considering aggregation of the stress-strain relations along certain control sections of the element. Fiber discretization of the sections accompanied by adequate material model ensures coupling of the stress resultants axial force, shear force, bending moment about both axes and torsion accurately. These attributes of the mixed element relax reliance on displacement approximations on the control sections of the beam element that are inevitable in displacement based elements. As a result, the element is free from shear-locking. Authentication and superiority of the proposed 3d element are displayed by comparing the ability of the mixed element to capture nonlinear coupling of axial, shear force, bending moments and torsion with the results of the similar 3d displacement based elements and exact solutions that are readily available in the literature. Moreover, linear elastic free vibration analyses of the proposed mixed element are carried out by using the flexibility based consistent mass matrix that is also derived in this study and it is pointed out that 3d mixed element has the ability of determining not only the fundamental vibration frequency but also higher order frequencies with a considerable accuracy by using only a couple of elements per member span.


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Citation Formats
O. Soydaş, “A Three dimensional mixed formulation nonlinear frame finite element based on hu-washizu functional,” Ph.D. - Doctoral Program, Middle East Technical University, 2013.