Mathematical Sciences: Symmetry Methods and Nonlinear Analysis in Elastomechanics

研究人员将研究具有对称性的微分方程及其在固体力学中的应用。 这些应用涉及非线性弹性和粘弹性固体和结构的几何精确公式。 这项工作的目标是发现新现象，并进一步发展和利用椭圆方程解的对称性和节点性质之间的联系，特别是在全局分岔和连续问题的背景下。 结构弯曲的方式可以在数学上描述为描述结构的方程的解。 通常，弯曲取决于一个参数，例如结构上的载荷。如果随着载荷的变化，结构对于相同的载荷可以以不同的方式弯曲，那么解决方案被认为在该载荷值处分叉。 分叉的全局描述通常很难获得，但非常有价值。当结构对称时，这些对称性可用于更好地掌握全局行为。 应用不仅适用于分析结构，还适用于研究材料本身的行为。

The investigator will study differential equations with symmetry and applications to solid mechanics. The applications involve geometrically exact formulations of nonlinearly elastic and viscoelastic solids and structures. The goals of the work are to detect new phenomena and to further develop and exploit the connection between symmetry and nodal properties of solutions of elliptic equations, particularly in the context of global bifurcation and continuation problems. The way that structures bend can be described mathematically as the solution of equations describing the structure. Often the bending depends on a parameter, for instance the load on the structure, If as the load varies the structure can bend in different ways for the same load, then the solutions are said to bifurcate at that value of the load. Global descriptions of the bifurcations are generally hard to get, but are very valuable. When the structure is symmetric, those symmetries can be used to get a better grip on the global behavior. Applications arise not only in analysing structures but also in studying the behavior of materials themselves.