A BEM approach to the evaluation of warping functions in the Saint Venant theory

Paradiso, Massimo; Vaiana, Nicolò; Sessa, Salvatore; Marmo, Francesco; Rosati, Luciano

doi:10.1016/j.enganabound.2020.01.004

Cited by 10 publications

(4 citation statements)

References 54 publications

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“…[20] used the complex variable boundary element method to evaluate shear stress caused by torsion and flexure in beams. Paradiso, M. [21] introduced a numerical method based on the boundary element method to determine shear stress in the Saint Venant theory of beam. A boundary approach labeled line element-less method was recently shown to solve the Saint Venant's flexure-torsion problem for isotropic material and arbitrary cross-sections by Di Paola, M. et al [22].…”

Section: Introductionmentioning

confidence: 99%

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

2021

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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.

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Section: Introductionmentioning

confidence: 99%

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

2021

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“…Besides the finite difference and finite element method, many authors have applied other numerical methods such as the boundary element method (BEM) [11][12][13][14][15][16], line element-less method (LEM) [17][18], a null-field integral technique [19], and finite-volume method [20][21] to analyse the torsion problem. Katsikadelis, J. T. et al [11] examined the torsion of general composite bars by BEM while Gaspari, D. et al [12] tackled orthotropic beams with a polygonal cross-section.…”

Section: Introductionmentioning

confidence: 99%

“…et al [14] obtained a new BEM from the general Cauchy integral formula derived from the Borel-Pompeiu formula to analyse the torsion problem. Paradiso, M. et al [15] achieved an efficient method to determine the warping function parameter with the general cross-section. Chen, K. H. et al [16] introduced a new error estimation technique in BEM to optimise the torsion problem with a multiply-connected domain.…”

Section: Introductionmentioning

confidence: 99%

Torsional Shear Stress in Prismatic Beams With Arbitrary Cross-Sections Using Finite Element Method

Tran¹

2021

CEJ

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Determining the shear stress of a structural element caused by torsion is a vital problem. The analytical solution of the Saint-Venant torsion is only suitable for simple cross-sections. The numerical method to evaluate the shear stress of complicated cross-sections is indispensable. Many numerical methods have been studied by scientists. Among these studies, Gruttmann proposed an excellent numerical method, which inherited the Saint-Venant theory. However, the use of isoparametric four-noded quadrilateral elements made the method not to reach the best optimization. The objective of this paper is to improve Gruttmann‘s method by using isoparametric eight-noded quadrilateral elements. MATLAB is the language for programming the numerical method. The validated examples have demonstrated that the author’s numerical method is more effective than Gruttmann‘s method.

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“…However, the solution using shell or solid elements is still not more flexible and computationally efficient than determining the stress on the cross-section by superimposition technique, 2D cross-section, and 1D beam element. BEM has quickly developed in recent years and has been considered as FEM's rival [35]. However, the world's leading structural analysis software companies [36] still use FEM primarily.…”

Section: Introductionmentioning

confidence: 99%

Shear Lag Analysis due to Flexure of Prismatic Beams with Arbitrary Cross-Sections by FEM

Tran¹,

Navrátil²

2021

Period. Polytech. Civil Eng.

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This paper presents the use of a finite element method (FEM) to analyze the shear lag effect due to the flexure of beams with an arbitrary cross-section and homogeneous elastic material. Beams are constrained by the most common types of supports, such as fixed, pinned, and roller. The transverse, concentrated, or distributed loads act on the beams through the shear center of the cross-section. The presented FEM transforms the 3D analysis of the shear lag phenomenon into separated 2D cross-sectional and 1D beam modeling. The characteristics of the cross-section are firstly derived from 2D FEM, which uses a 9-node isoparametric element. Then, a 1D FEM, which uses a linear isoparametric element, is developed to compute the deflection, rotation angle, bending warping parameter, and stress resultants. Finally, the stress field is obtained from the local analysis on the 2D-cross section. A MATLAB program is executed to validate the numerical method. The validation examples have proven the efficiency and reliability of the numerical method for analyzing shear lag flexure, which is a common problem in structural design.

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A BEM approach to the evaluation of warping functions in the Saint Venant theory

Cited by 10 publications

References 54 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

Torsional Shear Stress in Prismatic Beams With Arbitrary Cross-Sections Using Finite Element Method

Shear Lag Analysis due to Flexure of Prismatic Beams with Arbitrary Cross-Sections by FEM

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