On fractional bending of beams

被引：34

作者：

Lazopoulos, K. A. ^{[1
]}

Lazopoulos, A. K. ^{[2
]}

机构：

[1] 14 Theatrou Str, Rafina 19009, Greece

[2] Hellen Army Acad, Dept Math Sci, Vari 16673, Greece

来源：

ARCHIVE OF APPLIED MECHANICS | 2016年 / 86卷 / 06期

关键词：

Fractional tangent space; Fractional differential geometry; Curvature vector; Fractional bending; Euler-Bernoulli bending principle; A cantilever beam; CALCULUS;

D O I：

10.1007/s00419-015-1083-7

中图分类号：

O3 [力学];

学科分类号：

08 ; 0801 ;

摘要：

Clarifying the geometry of the fractional tangent space of a curve, fractional differential geometry of curves has already been revisited, Lazopoulos and Lazopoulos (2015), defining also the curvature vector. Fractional bending of a beam is introduced, applying Euler-Bernoulli bending principle. The proposed theory is implemented to the bending deformation of a cantilever beam under continuously distributed loading.

引用

页码：1133 / 1145

页数：13

共 19 条

[11]

Lazopoulos K.A., 2015, ADV THEOR MATH UNPUB

[12]

Leibniz GW., 1849, LEIBNITZEN MATH SCHR, V2, P301

[13]

Liouville J., 1832, Journal de lcole Polytechnique, Paris, V13, P71

[14]

Porteous IR., 1994, Geometric differentiation-for the intelligence of curves and surfaces

[15]

Riemann B., 1876, GESAMMELTE WERKE, V62

[16]

Samko A. A., 1993, Fractional Integrals andDerivatives: Theory and Applications

[17] Fractional vector calculus and fractional Maxwell's equations [J].

Tarasov, Vasily E. .

ANNALS OF PHYSICS, 2008, 323 (11) :2756-2778

[18]

Tarasov VE, 2011, NONLINEAR PHYS SCI, P1

[19]

Truesdell C., 1977, A first course in rational continuum mechanics, V1

← 1 2 →