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Published in:
2019 | OriginalPaper | Chapter
On the Quasi-Static Approximation to the Initial Traction Boundary Problem of Linear Elastodynamics
Author : Robin J. Knops
Published in: New Achievements in Continuum Mechanics and Thermodynamics
Publisher: Springer International Publishing
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Conditions are investigated that are suffcient for the quasi-static approximation to be valid in the initial traction boundary value problem of linear elastodynamics on a bounded three-dimensional spatial region. The approach consists of two main steps both of which involve trace inequalities to derive explicit estimates. The first establishes continuous dependence of the solution upon the inertia. The second treats continuous dependence of the inertia upon surface traction and body-force. Circumstances when the approximation is not valid are briefly discussed.