Volumetric growth of an elastic body may give rise to residual stress. Here a rigorous analysis of the residual strains and stresses generated by growth in the axisymmetric Kirchhoff plate is given. Balance equations are derived via the global constraint principle, growth is incorporated via a multiplicative decomposition of the deformation gradient, and the system is closed by a response funct...

In this paper, we study the asymptotic behavior of solutions to Kirchhoff type stochastic plate equation driven by additive noise defined on unbounded domains. We first prove uniform estimates and then establish existence upper semicontinuity random attractors.

This paper proposes a pseudospectral approach for the Kirchhoff plate bending problem with uncertainties. The Karhunen-Loève expansion is used to transform the original problem to a stochastic fourth-order PDE depending only on a finite number of random variables. For the latter problem, its exact solution is approximated by a gPC expansion, with the coefficients obtained by the sparse grid met...

Abstract. Consider a Kirchhoff plate ∂2 t u+Δ 2u−∂2 t Δu = 0 in Ω× (0, T ), with boundary data u = Δu = 0 on ∂Ω×(0, T ) and unknown initial data u(·, 0) = u0 and ∂tu(·, 0) = u1 in Ω. We study an inverse problem of determining (u0, u1) from an interior observation u|ω×(0,T ). Here Ω is a bounded domain, ω a nonempty open subset of Ω, and T > 0 a suitable time duration. By means of an iterative t...

Abstract. This work presents a numerical framework for long dynamic simulations of structures made multiple thin shells undergoing large deformations. The C1-continuity requirement the Kirchhoff-Love theory is met in interior patches by cubic NURBS approximation functions with membrane locking avoided patch-wise reduced integration. A simple penalty approach coupling adjacent patches, applicabl...

geometrically nonlinear governing equations for a plate with linear viscoelastic material are derived. the material model is of boltzmann superposi¬tion principle type. a third-order displacement field is used to model the shear deformation effects. for the solution of the nonlinear governing equations the dynamic relaxation (dr) iterative method together with the finite difference discretizati...

We study the problem describing incidence of a plane wave on semiinfinite thin Kirchhoff plate with periodic traction-free-edge. prove that any perturbation boundary, except for straight cracks parallel to generates trapped mode provided angle is not zero.

We present a comprehensive rotation-free Kirchhoff-Love (KL) shell formulation for peridynamics (PD) that is capable of modeling large elasto-plastic deformations and fracture in thin-walled structures. To remove the need predefined global parametric domain, Principal Component Analysis employed meshfree setting to develop local parameterization midsurface. The KL kinematics utilized correspond...