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.


An accurate nonlinear 3d Timoshenko beam element based on Hu-Washizu functional
Soydas, Ozan; Sarıtaş, Afşin (Elsevier BV, 2013-09-01)
An accurate 3d mixed beam element that is efficient especially in nonlinear analysis is presented in this paper. The mathematical theory is based on Hu-Washizu principle that uses three-fields in the variational form. The composition of the variational form ensures independent selection of displacement, stress and strain fields. Timoshenko beam theory is extended to three dimensions for deriving strains from displacement field. Numerical integration of stress strain relations along control sections is carri...
A New modal superposition method for nonlinear vibration analysis of structures using hybrid mode shapes
Ferhatoğlu, Erhan; Özgüven, Hasan Nevzat; Ciğeroğlu, Ender; Department of Mechanical Engineering (2017)
In this thesis, a new modal superposition method based on a hybrid mode shape concept is developed for the determination of steady state vibration response of nonlinear structures. The method is developed specifically for systems having nonlinearities where the stiffness of the system may take different limiting values. Stiffness variation of these nonlinear systems enables one to define different linear systems corresponding to each value of the limiting equivalent stiffness. Moreover, the response of the ...
A hybrid stress element for thin-walled beams
Oral, Süha (2003-04-05)
A hybrid stress finite element for linear static analysis of thin-walled beams is presented. The element is based on Vlasov theory. The hybrid stress formulation is particularly suitable in this case where displacement assumption is not necessary and a simple polynomial assumption for independent stress resultants is sufficient to form the element stiffness matrix. The result is a simple and elegant element, which is accurate and cost effective. The formulation is assessed by analyzing a structure having op...
Nonlinear fiber modeling of steel-concrete partially composite beams with channel shear connectors
Öztürk, Alper; Baran, Eray; Department of Civil Engineering (2017)
The purpose of this study is to develop a nonlinear fiber-based finite element model of steel-concrete composite beams. The model was developed in OpenSees utilizing the available finite element formulations and the readily available uniaxial material constitutive relations. The model employed beam elements for the steel beam and the concrete slab, while zero-length connector elements were used for the steel-concrete interface. The channel shear connector response used in numerical models was based on the p...
Three dimensional frame element formulation for nonlinear analysis of semi rigid steel structures
Özel, Halil Fırat; Sarıtaş, Afşin; Karakaş, Zafer (null; 2016-09-21)
In this paper, a force-based three-dimensional frame finite element formulation with spread of inelasticity through the element and localized nonlinear semi-rigid connections is developed. The proposed model utilizes Euler-Bernoulli beam theory assumptions, and adopts fiber discretization of monitored sections along element length and section depth for the spread of inelasticity in order to capture axial force and biaxial bending moment interaction. Defining any type of semi-rigid either linear or nonlinear...
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.