Free vibration characteristics of a 3d mixed formulation beam element with force-based consistent mass matrix

Soydas, Ozan; Saritas, Afsin

doi:10.1177/1077546315619263

Cited by 4 publications

(4 citation statements)

References 37 publications

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“…Eleman formulasyonunda konsol sistemin kütlesi, elemanın uzunluğu boyunca yayılı yük kabul edilmiş ve yayılı kütle matrisi, kesit kütle matrisinden Soydaş ve Sarıtaş [27] tarafından sunulduğu şekilde oluşturulmuştur. Bu matrise bu çalışma kapsamında yarı-rijit bağlantıların sunduğu esnekliğin Eş.…”

Section: Kuvvet Bazlı Yayılı Kütle Matrisi (Force Based Consistent Ma...unclassified

Kiriş-Kolon ve Kolon-Taban Yarı-Rijit bağlantılı çelik yapıların doğrusal olmayan ve titreşim analizleri için çerçeve sonlu elemanı modeli

ÖZEL

SARITAŞ

2022

Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi

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 A frame finite element based on force-based formulation with shear deformations  Application of linear or non-linear semi-rigid connection will not increase the degrees of freedom.  Force-based consistent mass matrix with semirigidity in connections and an appropriate shear correction coefficient for I-sections Figure A. Nonlinear Behavior of Steel Structures with Semi-Rigid Connections a) 2D 6 Stories Steel Frame, b) 3D Triangular Planar Steel Frame, c) 3D 6 Stories Steel FramePurpose: The purpose of this study is to develop and implement an accurate and robust frame finite element model for nonlinear structural analysis and vibration estimation of steel framed structures with semi-rigid connections. Theory and Methods:A frame finite element with semi-rigid connections based on force-based formulation and considering shear deformations is derived to obtain the nonlinear behavior of steel structures with high accuracy. Distributed plasticity approach is defined along each element length and over the depth of each section, and linear or nonlinear semi-rigid connection behavior can be specified anywhere along elements without the necessity to define additional nodes and to increase the degrees of freedom of the structural system. To perform vibration analyses with similar accuracy, force-based consistent mass matrix is used taking into account semi-rigidity in connections and an appropriate shear correction coefficient for I-sections. Results:First, a fix-fix supported beam with semi-rigid connections at its ends is acted on by a distributed load in order to observe spread of plasticity along beam length and connection regions. After this example, 2D and 3D complex and irregular steel frame structures with or without semi-rigid connections are analyzed and the performance of the element is compared with benchmark solutions. Finally, results of the modal analysis of a steel framed structure with semi-rigid connections is compared with a widely used structural analysis program. Conclusion:Proposed frame element with semi-rigid connections provides accurate, robust and practical modeling and nonlinear analysis of steel framed structures under extreme loading conditions. In the presented examples, it was possible to push the structures to higher displacement values than the existing results, and it was revealed that the non-linear behavior in the column-base connections could create much more critical results for the structural systems with P-Delta effects. In addition, high-level accuracy results were obtained when performing vibration analyses with the application of force-based consistent mass matrix.

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Section: Kuvvet Bazlı Yayılı Kütle Matrisi (Force Based Consistent Ma...unclassified

Kiriş-Kolon ve Kolon-Taban Yarı-Rijit bağlantılı çelik yapıların doğrusal olmayan ve titreşim analizleri için çerçeve sonlu elemanı modeli

ÖZEL

SARITAŞ

2022

Gazi Üniversitesi Mühendislik Mimarlık Fakültesi Dergisi

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“…[16] presented a method for evaluating the shape functions and structural matrices derived for non-prismatic Euler-Bernoulli beam elements. [17] analyzed non-prismatic Timoshenko beams using a basic displacement function. [18] used a force-based approach to derive a three-dimensional consistent mass matrix for vibration analysis of beams.…”

Section: Introductionmentioning

confidence: 99%

An Alternative Approach to Obtaining Stiffness and Mass Matrices for Three-Dimensional Bernoulli-Euler and Timoshenko Beam-Columns

Aydin¹

2021

J. Civ. Eng. Constr.

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In the static analysis of beam-column systems using matrix methods, polynomials are using as the shape functions. The transverse deflections along the beam axis, including the axial- flexural effects in the beam-column element, are not adequately described by polynomials. As an alternative method, the element stiffness matrix is modeling using stability parameters. The shape functions which are obtaining using the stability parameters are more compatible with the system’s behavior. A mass matrix used in the dynamic analysis is evaluated using the same shape functions as those used for derivations of the stiffness coefficients and is called a consistent mass matrix. In this study, the stiffness and consistent mass matrices for prismatic three-dimensional Bernoulli-Euler and Timoshenko beam-columns are proposed with consideration for the axial-flexural interactions and shear deformations associated with transverse deflections along the beam axis. The second-order effects, critical buckling loads, and eigenvalues are determined. According to the author’s knowledge, this study is the first report of the derivations of consistent mass matrices of Bernoulli-Euler and Timoshenko beam-columns under the effect of axially compressive or tensile force.

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“…Extension of the models including cross-section warping effects to the dynamic field requires the definition of the consistent element mass matrix [9]. This is straightforward for classic displacement-based FEs, but results more involved in force-based and mixed FE formulations [10].…”

Section: Introductionmentioning

confidence: 99%

“…This is straightforward for classic displacement-based FEs, but results more involved in force-based and mixed FE formulations [10]. The procedure proposed in [10] was recently introduced in enhanced models by [9,11].…”

Section: Introductionmentioning

confidence: 99%

Non Linear Dynamic Analysis of Thin-Walled Structures Adopting a Mixed Beam Finite Element Model With Out-of-Plane Cross-Section Warping

Re¹,

Addessi²,

Paolone³

2019

Proceedings of the 7th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

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This paper focuses on the dynamic response of thin-walled structural elements. A mixed three-dimensional (3D) beam formulation is adopted, that includes the effect of inertia forces under dynamic loading conditions and accounts for out-of-plane cross-section warping. This is introduced by adding a specific displacement field to those due to rigid body motions, and is interpolated in the element volume with the definition of specific shape functions. The element governing equations are derived by expressing the Lagrangian functional in terms of four independent fields, i.e. the material rigid displacements, the strains and stresses and the additional warping displacement field. Four Lagrange's equations of motion result, corresponding to the element compatibility condition enforced in weak form, the material constitutive law, and two sets of element equilibrium conditions associated to the rigid and warping displacements, respectively. The FE model has been implemented in a standard numerical code and used to investigate the effect of cross-section warping on the dynamic response of thin-walled structures. A T-shape beam is analyzed by performing modal decomposition and time-history analyses under linear elastic and nonlinear constitutive behavior. 3611 COMPDYN 2019 7 th ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering M. Papadrakakis, M. Fragiadakis (eds.

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Free vibration characteristics of a 3d mixed formulation beam element with force-based consistent mass matrix

Cited by 4 publications

References 37 publications

Kiriş-Kolon ve Kolon-Taban Yarı-Rijit bağlantılı çelik yapıların doğrusal olmayan ve titreşim analizleri için çerçeve sonlu elemanı modeli

Kiriş-Kolon ve Kolon-Taban Yarı-Rijit bağlantılı çelik yapıların doğrusal olmayan ve titreşim analizleri için çerçeve sonlu elemanı modeli

An Alternative Approach to Obtaining Stiffness and Mass Matrices for Three-Dimensional Bernoulli-Euler and Timoshenko Beam-Columns

Non Linear Dynamic Analysis of Thin-Walled Structures Adopting a Mixed Beam Finite Element Model With Out-of-Plane Cross-Section Warping

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