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The coupled equations of fluid motion and pipe displacement are solved.
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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.
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.
Equations obtained by applying the principle of virtual displacements were solved in a closed form using double trigonometric series.
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.
Nonlinear governing equations are obtained based on the static version of virtual displacements and are solved via the multi-term Galerkin method.
For this purpose, exact displacement shape functions are solved from the differential equilibrium equation, by using arbitrary boundary conditions.
An unstructured finite volume time domain method (UFVTDM) is proposed to simulate stress wave propagation, in which the original variables of displacement and stress are solved based on the dynamic equilibrium equations.
The governing equilibrium equations are derived analytically from the Principle of Virtual Displacements (PVD), and are solved exactly referring to the Lévy-type procedure.
The two coupled ordinary differential equations in terms of displacement and electric potential are solved analytically.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com