Stationary Dynamic Displacement Solutions for a Rectangular Load Applied within a 3D Viscoelastic Isotropic Full Space—Part I: Formulation

<table class="table-group" width="800px"><tr class="fig-image" id="a"><td><img alt="216297.fig.001a" src="https://static-preview.hindawi.com/articles/mpe/volume-2012/216297/figures/216297.fig.001a.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(a) </b>first BVP load <svg height="13.3" id="M3" style="vertical-align:-3.50804pt" version="1.1" viewbox="0 0 19.4125 13.3" width="19.4125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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t37 -108zM482 289q0 114 -113 114q-26 0 -66 -7l-70 -327q12 -14 32 -25t39 -11q59 0 118.5 81.5t59.5 174.5z" id="x1D45D"></path></g>
<g transform="matrix(.012,-0,0,-.012,10.138,12.95)"><path d="M698 636l-541 -596q60 -5 176 -5q91 0 138.5 5t69.5 24q44 36 85 124l29 -15q-38 -125 -64 -173h-559l-9 16l545 598h-182q-81 0 -109 -8t-48 -31q-26 -29 -55 -103l-29 3q23 86 42 200h22q11 -16 21 -20.5t34 -4.5h428z" id="x1D44D"></path></g>
</svg></td></tr></table></td></tr><tr class="fig-image" id="b"><td><img alt="216297.fig.001b" src="https://static-preview.hindawi.com/articles/mpe/volume-2012/216297/figures/216297.fig.001b.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(b) </b>second BVP load <svg height="13.3" id="M4" style="vertical-align:-3.50804pt" version="1.1" viewbox="0 0 18.9125 13.3" width="18.9125" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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q8 -26 43 -107.5t61 -134.5q114 145 174 240q14 24 8 33t-37 13l-34 4l8 28h238z" id="x1D44C"></path></g>
</svg></td></tr></table></td></tr><tr class="fig-image" id="c"><td><img alt="216297.fig.001c" src="https://static-preview.hindawi.com/articles/mpe/volume-2012/216297/figures/216297.fig.001c.jpg"/></td></tr><tr class="fig-caption"><td align="center"><table><tr><td><b>(c) </b>third BVP load <svg height="13.3" id="M5" style="vertical-align:-3.50804pt" version="1.1" viewbox="0 0 20.25 13.3" width="20.25" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink">
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l-110 215q-26 51 -44 63t-72 17l6 28h250l-6 -28l-27 -4q-30 -5 -35 -10t3 -27q17 -43 95 -190q70 78 154 185q15 21 10 29.5t-33 12.5l-30 4l5 28h236z" id="x1D44B"></path></g>
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<table>Traction loadings for the three boundary value problems.</table>

Mathematical Problems in Engineering

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Figure 1

Figure 1: Stationary Dynamic Displacement Solutions for a Rectangular Load Applied within a 3D Viscoelastic Isotropic Full Space—Part I: Formulation 