Qualitative Methods in Continuum Mechanics
The widespread use of computers in difficult branches of continuum mechanics makes it valuable to draw general conclusions from particular solutions, so that these can be used to estimate quantities of interest instead of having to solve them in detail. This book examines these techniques, using integral solutions, and looks in particular at seepage theory and fracture mechanics.
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Qualitative methods and bounds for flows of viscoplastic fluids through
Elasticity theory Hookes law
Elasticity theory The energy theorems and some energy bounds
7 other sections not shown
applied arbitrary asymptotic Barenblatt boundary conditions boundary value problem cavity circular crack comparison theorem components Consider const constant contact zone Corollary corresponding crack contour crack G crack growth crack problem crack surfaces crack volume curve decrease deformation energy derived displacement elastic body elastic energy elasticity problem elasticity theory elliptic equal equation equilibrium estimates expressed extremal contour extremum field flow discharge flow domain fluid fracture fracture mechanics free boundary Goldstein and Shifrin Goldstein R. V. half-space harmonic function Hence hodograph homogeneous hydraulic head impervious implies initial inlet integral isoperimetric inequality Lemma linear loads lower bound Lur'e maximum principle Mekh minimum parameter plane X3 Polubarinova-Kochina Polya and Szego porous medium prescribed pressure differential pressure gradient proof properties Proposition Publ radius region G reservoir Russian Section seepage law segment solution stagnant zone statement stress intensity factor symmetrization tensor torsion problem variation vector