A numerical method for the exact elastic beam theory. Applications to homogeneous and composite beams

Fatmi, Rached El; Zenzri, Hatem

doi:10.1016/j.ijsolstr.2003.12.011

Cited by 42 publications

(38 citation statements)

References 13 publications

(18 reference statements)

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“…Only in the case of m ¼ 0 the results of various definitions coincide with those of the engineering beam theory. Moreover, the convergence of the obtained results employing the proposed numerical procedure with those obtained from 2-D FEM solutions [19], [26] applied to the same energy formulation and from a 3-D FEM solution [31] applied to the 'exact' elastic beam theory is easily verified. In Figs.…”

Section: Examplementioning

confidence: 68%

“…In Table 1 the shear deformation coefficients a z for various values of the Poisson's ratio ı´and the side ratio b=h are presented as compared with those obtained from a 3-D FEM solution [31] of the 'exact' elastic beam theory [29], from a 2-D FEM solution exploiting the principle of minimum potential energy [19], [26] and from the Cowper's definition. From this table the significant influence of the side ratio b=h of the rectangular section to the values of the deformation coefficients a z , contrary to the Cowper's definition is remarkable.…”

Section: Examplementioning

confidence: 99%

See 1 more Smart Citation

A BEM solution to transverse shear loading of beams

Sapountzakis

Mokos

2005

Comput Mech

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In this paper a boundary element method is developed for the solution of the general transverse shear loading problem of beams of arbitrary simply or multiply connected constant cross section. The analysis of the beam is accomplished with respect to a coordinate system that has its origin at the centroid of the cross section, while its axes are not necessarily the principal ones. The transverse shear loading is applied at the shear center of the cross section, avoiding in this way the induction of a twisting moment. Two boundary value problems that take into account the effect of Poisson's ratio are formulated with respect to stress functions and solved employing a pure BEM approach, that is only boundary discretization is used. The evaluation of the transverse shear stresses at any interior point is accomplished by direct differentiation of these stress functions, while both the coordinates of the shear center and the shear deformation coefficients are obtained from these functions using only boundary integration. Numerical examples with great practical interest are worked out to illustrate the efficiency, the accuracy and the range of applications of the developed method. The accuracy of the proposed shear deformation coefficients compared with those obtained from a 3-D FEM solution of the 'exact' elastic beam theory is remarkable.

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Section: Examplementioning

confidence: 68%

Section: Examplementioning

confidence: 99%

A BEM solution to transverse shear loading of beams

Sapountzakis

Mokos

2005

Comput Mech

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“…The accuracy of the proposed shear deformation coefficients compared with those obtained from a 3-D FEM solution of the ÔexactÕ elastic beam theory (Fatmi and Zenzri, 2004) is remarkable.…”

Section: Nomenclaturementioning

confidence: 86%

“…In this reference the shear problem is formulated with respect to the principal bending axes system, which as it is stated below is different from the principal shear axes one, while the evaluation of the non-diagonal shear deformation coefficient is missing. Moreover, Fatmi and Zenzri (2004) based on the ÔexactÕ elastic beam theory presented a numerical solution of the shear problem of composite beams of arbitrary crosssection employing the 3-D FEM. The last two references take into account the boundary conditions at the interfaces in contrast with all other research efforts in composite beams of arbitrary cross-section that ignore them (Pilkey, 2002), resulting in an analysis that is not completely rigorous.…”

Section: Nomenclaturementioning

confidence: 99%

A BEM solution to transverse shear loading of composite beams

Mokos

Sapountzakis

2005

International Journal of Solids and Structures

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“…The stress field is dependent on a fully three-dimensional function. The ''exact'' beam theory has been applied to compute the stress field of bars under traction boundary conditions, using FEM [4][5][6]. Based on the ''exact'' beam theory and neglecting the Poisson effect, El Fatmi [7] formulated a nonuniform warping theory of bars employing twodimensional St. Venant warping functions and one-dimensional independent warping parameters and provided two alternatives so as to compute shear stresses.…”

Section: Introductionmentioning

confidence: 99%