Quadratic B-splines in the analog equation method for the nonuniform torsional problem of bars

Sapountzakis, E. J.; Tsiptsis, Ioannis N.

doi:10.1007/s00707-014-1143-z

Cited by 9 publications

(8 citation statements)

References 10 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…I N ξ η of this element can be described as follows: Inserting the derivatives of (ω T ) h , η h and (ω B ) h , into the weak forms of ( 7) and (18), respectively, yields the finite element equations…”

Section: Finite Element Discretizationmentioning

confidence: 99%

See 1 more Smart Citation

An Efficiency Method for Assessment of Shear Stress in Prismatic Beams with Arbitrary Cross-Sections

2021

View full text Add to dashboard Cite

The dimensions of a bearing structure tend to be designed as slender as possible to ensure aesthetics and to save material, which makes the structure more susceptible to damage caused by shear forces. When the structure is subjected to an earthquake, the shear failure is even the primary mode of failure. Research on shear stress has always been of great interest to scientists. This paper presents an efficient method for the assessment of the shear stress for prismatic beams with arbitrary cross-section. The numerical method implemented in a MATLAB environment is validated by analyzing five examples. The study shows the efficiency and reliability of the numerical method, which allows for more precise analysis and design of cross-sections. Therefore, significant savings of material can be reached, which will have a positive impact on our environment and which can help sustainable growth.

show abstract

Section: Finite Element Discretizationmentioning

confidence: 99%

“…Sapountzakis, E.J. et al [18,19] proposed the nonuniform torsion solution and the general transverse shear loading problem of beams of the arbitrary cross-section with the boundary element method. Barone,G.…”

Section: Introductionmentioning

confidence: 99%

An Efficiency Method for Assessment of Shear Stress in Prismatic Beams with Arbitrary Cross-Sections

2021

View full text Add to dashboard Cite

show abstract

“…In this study, the properties of smooth NURBS functions are examined and, for a given spectrum of frequencies (given number of degrees of freedom and bandwidth) the improved accuracy in spectral calculations over classical finite elements analysis is demonstrated. In addition to this, the introduction of B-splines in a BEM based technique has only been examined by Sapountzakis and Tsiptsis (2014) for the static nonuniform torsional problem of bars as well as for the static generalized warping analysis of beams (Sapountzakis and Tsiptsis, 2016). Recently, novel isogeometric tools were used in FEM for the vibration analysis of straight nonlinear Euler–Bernoulli beam (Weeger et al., 2013).…”

Section: Introductionmentioning

confidence: 99%

Generalized vibration analysis of beams including warping effects by isogeometric methods

Sapountzakis

Tsiptsis

2017

Journal of Vibration and Control

View full text Add to dashboard Cite

In this paper, the Isogeometric tools, either integrated in the Finite Element Method (FEM) or in a Boundary Element based Method (BEM) called Analog Equation Method (AEM), are employed for the vibration analysis of homogeneous beams of arbitrary cross section (thin- or thick- walled) taking into account nonuniform warping and shear deformation effects (shear lag due to both flexure and torsion). The beam is subjected to the combined action of arbitrarily distributed or concentrated axial and transverse loading, as well as to bending, twisting and warping moments. Its edges are subjected to the most general boundary conditions. By employing a distributed mass model system accounting for longitudinal, transverse, rotatory, torsional and warping inertia, ten boundary value problems with respect to the variable along the beam time-dependent 1-D kinematical components are formulated. The numerical solution or the spectrum analysis of the aforementioned problems is performed through IGA, FEM and AEM, leading to a system of second-order differential equations, which are quasi-static and solved for the free vibration case, formulating a generalized eigenvalue problem. Special cases of the generalized problem have also been studied in order to demonstrate the efficiency of AEM in reducing computational effort and improving accuracy, especially when combined to Isogeometric tools, such as NURBS and B-splines.

show abstract

“…The numerical solution of the curved advanced beam is based on B-splines [36][37] and NURBS (Isogeometric Analysis) offering the advantage of integrating computer aided design (CAD) in the analysis.…”

Section: Introductionmentioning

confidence: 99%

Isogeometric Methods in Dynamic Analysis of Curved Beams Including Warping and Distortional Effects

Tsiptsis¹,

Sapountzakis²

2017

Proceedings of the 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COM

View full text Add to dashboard Cite

show abstract

Quadratic B-splines in the analog equation method for the nonuniform torsional problem of bars

Cited by 9 publications

References 10 publications

An Efficiency Method for Assessment of Shear Stress in Prismatic Beams with Arbitrary Cross-Sections

An Efficiency Method for Assessment of Shear Stress in Prismatic Beams with Arbitrary Cross-Sections

Generalized vibration analysis of beams including warping effects by isogeometric methods

Isogeometric Methods in Dynamic Analysis of Curved Beams Including Warping and Distortional Effects

Contact Info

Product

Resources

About