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<p class="MsoNormal" align="center" style="margin-bottom:6.0pt;text-align:center;
line-height:115%"><b><span style="font-size: 17pt; line-height: 115%; font-family: Arial; ">PhD
Dissertation <o:p></o:p></span></b></p>
<p class="MsoNormal" align="center" style="margin-bottom:6.0pt;text-align:center;
line-height:115%"><span style="font-size: 17pt; line-height: 115%; font-family: Arial; ">Shengyou Yang<o:p></o:p></span></p>
<p class="MsoNormal" align="center" style="margin-bottom:6.0pt;text-align:center;
line-height:115%"><span style="font-size: 17pt; line-height: 115%; font-family: Arial; ">Surface Instability and Bifurcation of Elastic Materials<o:p></o:p></span></p>
<p class="MsoNormal" align="center" style="margin-bottom:6.0pt;text-align:center;
line-height:115%"><span style="font-size: 17pt; line-height: 115%; font-family: Arial; "> </span></p>
<p class="MsoNormal" style="margin-bottom:6.0pt;line-height:115%"><b><span style="font-family:Arial">Defense Time:</span></b><span style="font-family:Arial"> 10:00AM, Friday, December 4<sup>th</sup>, 2015<o:p></o:p></span></p>
<p class="MsoNormal" style="margin-bottom:6.0pt;line-height:115%"><b><span style="font-family:Arial">Location:</span></b><span style="font-family:Arial"> N137 Engineering Building 1<o:p></o:p></span></p>
<p class="MsoNormal" style="margin-bottom:12.0pt;line-height:115%"><b><span style="font-family:Arial">Committee
Members:</span></b><span style="font-family:Arial"> Prof. Yi-Chao Chen, Prof. Lewis
T. Wheeler, Prof. Pradeep Sharma, Prof. Yashashree Kulkarni, and Prof. Cumaraswamy Vipulanandan<o:p></o:p></span></p>
<p class="MsoNormal" style="margin-bottom:12.0pt;line-height:115%"><span style="font-family:Arial"> </span></p>
<p style="margin-top: 0in; margin-bottom: 12pt; text-align: justify; line-height: 115%; "><span style="font-family:Arial"> Surface
instabilities, such as wrinkles and creases, are often observed when elastic
materials are subject to a sufficiently large compression. This thesis investigates
surface instability and bifurcation of elastic materials due to their great
importance to engineering application. The surface instability is studied by using
the principle of minimum energy while the bifurcation is analyzed by solving
the linearized equilibrium equations. In this thesis, we focus on the surface
instability and bifurcation of a half-space, an infinite slab, and a
rectangular block of elastic materials subject to biaxial loading.<o:p></o:p></span></p>
<p class="MsoNormal" style="text-align:justify;text-justify:inter-ideograph;
line-height:115%;tab-stops:.5in 45.0pt"><span style="font-family:Arial;
mso-fareast-font-family:"Times New Roman";mso-fareast-language:ZH-CN"> For the problem of surface
instability, we use the first and second variations of the energy functional to
find the necessary condition for stability. The requirement of a positive
semi-definite second variation is transformed into the exploration of the
minimum value of a constrained integral. Then the first variation condition of
this constrained minimization problem leads to an eigenvalue problem associated
with the stability. Solution of the eigenvalue problem yields a characteristic
equation that determines the wavenumbers for the pattern of surface
instabilities and the corresponding critical loading parameters. Subsequent to
discussing the general properties of the characteristic equation, we obtain the
stability region analytically. For the bifurcation problem, we linearize the
boundary-value problem consisting of the Euler-Lagrange equation, the
constraint of incompressibility and the corresponding boundary conditions and
then solve the linearized boundary-value problem. Determination of non-trivial
solutions to the linearized boundary-value problem yields a characteristic
equation. Bifurcation points are obtained from the discussion of the general
properties of the characteristic equation. </span><span style="font-family:
Arial"><o:p></o:p></span></p>
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