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The hyper-singular boundary integral-differential equations of displacement and temperature discontinuities are obtained for a planar interfacial crack of an arbitrary shape.
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In the stress model, the governing equations of displacements within the adherends are formulated using the first-order laminated plate theory.
Equations of buckling displacement (buckling displacement is defined by the final displacement of the middle point of the pipelines), critical buckling force, and buckling stress (Mises stress) are proposed using the gene expression programming technique.
The coupling equation of displacement and impact load is solved through the Laplace transform, and the analytical solution for the transverse displacement is obtained.
Using Newton's second law and the Hooke's law, the equations of motion (displacement) for the tree components in Figure 7 can be formulated using second-order differential equations: (7).
Two differential equations of the displacements are derived for the case of an axially loaded adhesive single lap joint.
In this paper, to study the tilting motions of spindles, the Euler dynamic equations of angular displacements of spindles were proposed, and analytic solutions of the equations were also presented.
We present a block preconditioner for the efficient solution of the linear systems that arise when employing Newton's method to solve monolithically-coupled large-displacement fluid structure interaction problems in which the update of the moving fluid mesh is performed by the equations of large-displacement elasticity.
At first, three decoupled equations in terms of displacement components and three decoupled equations in terms of rotation components are obtained.
In order to find the solution for a nano-plate based on the presented formulation, one of the three equations in terms of displacement components and corresponding rotation equation should be solved independently.
The effects of stiffeneresultingial and dimequationsparameters are analyzed in detail.
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