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Direct stiffness method
About: Direct stiffness method is a research topic. Over the lifetime, 2584 publications have been published within this topic receiving 53131 citations.
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TL;DR: The structural characteristics of the human knee have been determined using the stiffness influence coefficient method, where the nonlinear load-displacement data is approximated by a least squares polynomial and differentiated to determine the stiffness coefficient as a function of displacement.
43 citations
TL;DR: In this article, a weighted-averaging frequency-domain finite-element method for 2D elastic wave modeling is presented. But the method is not suitable for the simulation of large-scale seismic inversion.
Abstract: We present a weighted-averaging frequency-domain finite-element method for an accurate and efficient 2D elastic wave modeling technique. Our method introduces three kinds of supplementary element sets in addition to a basic element set that is used in the standard finite-element method. By constructing global stiffness and mass matrices for four kinds of element sets and then averaging them with weighting coefficients, we obtain a new global stiffness and mass matrix. With optimal weighting coefficients determined by a Marquardt–Levenberg method to minimize grid dispersion and grid anisotropy, we can reduce the number of nodal points per shear wavelength from 33.3 (using the standard finite-element method) and 20 (using the eclectic method) to 5, with the errors of group velocities no larger than 1%. By reducing the number of grid points per wavelength, we achieve a 97% and 75% reduction of computer memory required to store the complex impedance matrix for a band-type matrix solver and a nested dissection method, respectively, compared with those of the eclectic method. Our method gives approximate solutions compatible with exact solutions for an infinite homogeneous, a semi-infinite homogeneous (Lamb9s problem), and a horizontal two-layer model with fewer grid points than the standard and the eclectic method. A major advantage of the weighted-averaging finite-element method for the elastic wave equation is that it provides solutions very close to correct solutions for Lamb9s problem economically, unlike most of the displacement approaches. In addition, our scheme makes the complex impedance matrix symmetric, which satisfies reciprocity. Seismic forward modeling techniques that satisfy reciprocity are of critical importance in seismic imaging and inversion because we can economically calculate a Jacobian matrix using the reciprocity. Successful simulation of a large-size model shows that our method can be used for the simulation of wave propagation in the geological model needed in the reverse-time migration or seismic inversion.
43 citations
TL;DR: In this article, the authors investigate a configuration comprising two positive stiffness elements and one negative stiffness element, which introduces hysteresis under a loading-unloading cycle, resulting in substantial energy dissipation, while maintaining stiffness.
42 citations
TL;DR: In this paper, the minimum collinear stiffness value (CSV) is applied for stiffness evaluation of machine tools with different kinematics types, and a dimensionless form is entered as the ratio of the CSV to the stiffness value of a single actuator.
42 citations
TL;DR: In this article, two analytical formulations of the tangent stiffness matrix are analyzed, the first using tendon lengths and forces, and the second using tendon length squared and force densities.
42 citations