To enable analytical solution, we need to investigate problems where the deformation gradient tensor is known precisely. We can then substitute it into the formula for stress as a function of the ...

IN the preface to his "Elliptic Functions", written in 1892, Prof. A. G. Greenhill complained that, although the subject was then nearly seventy years old, it had not made its way into the ordinary ...

The Jacobian is a matrix that approximates the deformation in a small volume around a point: stretching, scaling, and/or shearing. The Jacobian determinant is a scalar value that describes the local ...

Abstract: This paper focuses on using the Newton-Raphson method to solve the power-flow problems. Since the most computationally demanding part of the Newton-Raphson method is to solve the linear ...

Abstract: Deep integration of distributed energy brings great uncertainty into distribution network. Therefore, fast continuous power flow calculation plays a vital role in helping distribution ...

First-order derivatives: n additional function calls are needed. Second-order derivatives based on gradient calls, when the "grd" module is specified (Dennis and Schnabel 1983): n additional gradient ...