Search results for "Line integral"

Evaluation of Deflection of a Plate using Line Integrals

2014

The General Stokes’s Theorem

2012

Let ω be a differential form of degree k - 1 and class C 1 in a neighborhood of a compact regular k-surface with boundary M of class C 2. The general Stokes’s theorem gives a relationship between the integral of ω over the boundary of M and the integral of the exterior differential dω over M. It can be viewed as a generalization of Green’s theorem to higher dimensions, and it plays a role not unlike that of the fundamental theorem of calculus in an elementary course of analysis. Particular cases of the general Stokes’s theorem that are of great importance are the divergence theorem, which relates a triple integral with a surface integral and what we know as the classical Stokes’s theorem, w…

CVBEM for solving De Saint-Venant solid under shear forces

2013

Abstract Evaluation of shear stresses distribution due to external shear forces applied to De Saint-Venant beams has been solved through Complex Variable Boundary Element Method properly extended, to benefit from advantages of this method, so far widely used for twisted solids. Extending the above method, further simplifications have been introduced such as those of performing line integrals only, instead of domain integrals. Numerical applications confirm accuracy and efficiency of the proposed extended version of the method, since the good agreement with results proposed in literature.

Star-product approach to quantum field theory: The free scalar field

1990

The star-quantization of the free scalar field is developed by introducing an integral representation of the normal star-product. A formal connection between the Feynman path integral in the holomorphic representation and the star-exponential is established for the interacting scalar fields.

LEM for twisted re-entrant angle sections

2014

In this paper an innovative numerical method named as line element-less method, LEM, for finding solution of torsion problem has been extended to all shaped sections, including sections possessing re-entrant angles at their boundary. The response solution in terms of shear stress field or Prandtl function or warping function in all domain and for any kind of domain with arbitrary contour, may be performed quickly, calculating line integrals only. The method takes full advantage of the theory of analytic complex function and is robust in the sense that returns exact solution if this exists. Numerical implementation of LEM has been developed using Mathematica software without resorting to any…