Deducing the form factors for shear used in the calculus of the displacements based on strain energy methods. Mathematical approach for currently used shapes

5th ModTech International Conference - Modern Technologies in Industrial Engineering

Constantinescu, E.^1 ; Oanta, E.^2 ; Panait, C.^2

Constanta Maritime University, Faculty of Navigation and Naval Transport, 104 Mircea cel Batran Street, Constanta

900663, Romania^1

Constanta Maritime University, Faculty of Naval Electro-Mechanics, 104 Mircea cel Batran Street, Constanta

900663, Romania^2

关键词: Circular cross-sections;    Commercial applications;    Complex composites;    Computer-based instruments;    Geometrical characteristics;    Geometrical modeling;    Geometrical shapes;    Mathematical approach;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/227/1/012031/pdf
DOI  :  10.1088/1757-899X/227/1/012031

来源: IOP

【 摘 要 】

The paper presents an initial study concerning the form factors for shear, for a rectangular and for a circular cross section, being used an analytical method and a numerical study. The numerical study considers a division of the cross section in small areas and uses the power of the definitions in order to compute the according integrals. The accurate values of the form factors are increasing the accuracy of the displacements computed by the use of the strain energy methods. The knowledge resulted from this study will be used for several directions of development: calculus of the form factors for a ring-type cross section of variable ratio of the inner and outer diameters, calculus of the geometrical characteristics of an inclined circular segment and, using a Bool algebra that operates with geometrical shapes, for an inclined circular ring segment. These shapes may be used to analytically define the geometrical model of a complex composite section, i.e. a ship hull cross section. The according calculus relations are also useful for the development of customized design commands in CAD commercial applications. The paper is a result of the long run development of original computer based instruments in engineering of the authors.