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In computation of fluid-structure interactions, we use mesh update methods consisting of mesh-moving and remeshing-as-needed. When the geometries are complex and the structural displacements are large, it becomes even more important that the mesh moving techniques are designed with the objective to reduce the frequency of remeshing. To that end, we present here mesh moving techniques where the motion of the nodes is governed by the equations of elasticity, with selective treatment of mesh deformation based on element sizes as well as deformation modes in terms of shape and volume changes. We also present results from application of these techniques to a set of two-dimensional test cases.