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The implicit Euler time scheme is used, and the non-linear system giving the increment of the generalized nodal displacements is solved by the Newton-Raphson algorithm.
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Equations obtained by applying the principle of virtual displacements were solved in a closed form using double trigonometric series.
The differential equations describing the pile and soil displacements are solved using the Ritz method and the finite difference method, respectively, following an iterative numerical scheme.
The approximate solutions of displacements are solved for the first three terms, and the corresponding internal stresses can also be obtained.
The coupled equations of fluid motion and pipe displacement are solved.
The model equations for small amplitude stress fiber displacement were solved in response to forces applied either orthogonal to or in the direction of the stress fiber axis as depicted in Figure 1.
A solid material may be modelled using DEM by bonding particles together using contact models, and a force-displacement law is solved at the contacts.
Therefore, this multiphase scroll pump has the function of unloading gas liquid mixture pressure automatically during the compression process, so the frequently occurring problem of liquid slugging in displacement multiphase pumps is solved.
The coupling equation of displacement and impact load is solved through the Laplace transform, and the analytical solution for the transverse displacement is obtained.
The resulting boundary-value problem for the unknown jump in the particle displacement across the crack is solved by employing an integral equation approach.
The numerical solution of the aforementioned initial boundary value problem is performed through a BE method leading to a system of differential equations with displacement only unknowns, which is solved using an efficient direct time integration technique.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com