Variational base and solution strategies for non-linear force-based beam finite elements

This paper presents the variational bases for the non-linear force-based beam elements. The element state determination of these elements is obtained exactly from a two-field functional with independent stress and strain fields. The variational base of the non-linear force-based beam elements implemented in a general purpose displacement-based finite element program requires the inclusion of independent displacement field in the formulation. For this purpose, a three-field functional is considered with independent displacement, stress, and strain fields. Various local and global solution strategies come out from the mixed formulation of the beam element, and these are shown to yield the algorithms presented for non-linear force formulation beam elements in literature; thus removing any doubts on their variational bases. The presented numerical examples demonstrate the accuracy and robustness of the solution algorithms adapted for mixed formulation elements over popularly used displacement-based beam finite elements even for large structural systems.


Finite element modeling of beams with functionally graded materials
Gürol, Tolga; Sarıtaş, Afşin; Department of Civil Engineering (2014)
In this thesis a new beam element that is based on force formulation is proposed for modeling elastic and inelastic analysis of beams with functionally graded materials. The attempt of producing functionally graded materials (FGM) arose from mixing two materials in such a way that both of them preserve their physical, mechanical and thermal properties most effectively. FGM shows a gradation through the depth from typically a metallic material such as steel or aluminum at one face of the beam’s section depth...
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Sarıtaş, Afşin (2013-10-01)
This paper presents a mixed formulation frame element with the assumptions of the Timoshenko shear beam theory for displacement field and that accounts for interaction between shear and normal stress at material level. Nonlinear response of the element is obtained by integration of section response, which in turn is obtained by integration of material response. Satisfaction of transverse equilibrium equations at section includes the interaction between concrete and transverse reinforcing steel. A 3d plastic...
Domain-boundary element method for elastodynamics of functionally graded Timoshenko beams
Eshraghi, Iman; Dağ, Serkan (2018-01-15)
A new domain-boundary element method is developed for elastodynamic analysis of functionally graded Timoshenko beams. Three governing partial differential equations of motion are derived by considering through-the-thickness variations of the physical properties. Weighted-residual forms are imposed utilizing the static fundamental solutions. These forms are then reduced to three integral equations containing domain integrals with time derivatives of unknown functions. Through domain discretization and shape ...
Reduced order modeling of helicopter substructures for dynamic analysis
Hayırlı, Uğur; Kayran, Altan; Department of Aerospace Engineering (2018)
Dynamic analysis of a structure is generally conducted by the finite element method in aerospace structures. The models usually contain large number of elements to be able to obtain more accurate results. Although the most computers are capable of solving the large and complex problems, the analysis problems such as dynamic optimization, aeroelastic, frequency and time response may take long time due to involving iterative and multi-step processes. In this study, various model reduction methods are describe...
Least-squares finite element solution of Euler equations with H-type mesh refinement and coarsening on triangular elements
AKARGUN, Hayri Yigit; Sert, Cüneyt (2014-01-01)
Purpose - The purpose of this paper is to demonstrate successful use of least-squares finite element method (LSFEM) with h-type mesh refinement and coarsening for the solution of two-dimensional, inviscid, compressible flows.
Citation Formats
A. Sarıtaş, “Variational base and solution strategies for non-linear force-based beam finite elements,” INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, pp. 54–64, 2012, Accessed: 00, 2020. [Online]. Available: