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Variational Methods

abedford's picture

Hamilton's principle

I continue to receive inquiries about the monograph Hamilton's Principle in Continuum Mechanics, published in 1985 as Research Notes in Mathematics No. 139 by Pitman Publishing, Ltd. Now out of print, it is in the public domain and is attached here. My initial objective in writing it was to discuss the theoretical foundations of the applications of Hamilton's principle to mixtures that I had developed with D. S. Drumheller and others during the preceding decade.

MWR for the first- and third-order differential equations

Hi all,

In engineering sciences, we usually end up using either the second- or the fourth-order differential equations, and the MWR (the method of weighted residuals) works pretty well for them.

The question is: how about the first- and the third-order differential equations? Why don't we see any applications of MWR for these odd-ordered differential equations? What gives?

bazant's picture

Objective Stress Rates in Finite Strain of Inelastic Solid and Their Energy Consistency

In many practical problems of solid mechanics, it is sufficient to characterize material deformation by the small (or linearized) strain tensor. But there are also many problems where the finiteness of strain must be taken into account.

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