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In both cases, the only forces that act on a small material element are local and must propagate across the surface of the element.
The sound power radiated by the surface of the element is numerically determined from the vibrational pattern, offering an alternative for classical microphone measurements.
With this approach, the Riemann velocity at the nodes on the surface of the element, and the corresponding surface forces, are calculated by solving a multidirectional approximate Riemann problem in 2D Cartesian geometry.
The Riemann velocity at the nodes on the surface of the element, and the corresponding surface forces, are calculated by solving a multidirectional approximate Riemann problem using surfaces areas for axisymmetric coordinates.
The stiffeners are taken to be smeared over the surface of the element, and Hamilton's principle is used to derive the appropriate modifications which must be made to the shell differential equations and boundary conditions.
Advantages of cathodic protection, such as the possibility of preserving non-protective concrete and of reducing the invasiveness of the repair intervention, could be further improved by using small localised anodes, that do not affect the shape and surface of the element.
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Tie bars hold the elements together below the original surface of the elements.
Both elements use a modified right Cauchy-Green deformation tensor ¯¯¯C where five of its six components are linearly interpolated from values computed at the top and bottom surfaces of the element.
The objective of this paper is to determine these hourglass coefficients by matching exact solutions of pure bending and pure torsion applied in different directions on each of the surfaces of the element.
The total shadowed surface area of the element, contacting with air is S = 2(w + h) dx.
The procedure is designed to select and implement automatically the degrees of freedom in the domain (displacements) and on the boundary (surface forces) of the element to attain a prescribed level of accuracy.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com