Abstract
In this paper, a non-C0 double set parameter finite element method is presented for the clamped Kirchhoff plate with an elastic unilateral obstacle. A new high accuracy error estimate with order O(h2) in the broken energy norm is derived by use of a series of novel approaches, including some special features of the element and an incomplete biquadratic interpolation operator. At the same time, some experimental results are provided to verify the theoretical analysis.
Highlights
Let Ω ⊂ R2 be a bounded convex polygonal domain with a Lipschitz continuous boundaryΓ
Assume that the plate is subject to a load f ∈ L2 (Ω), f ≤ 0 a.e. in Ω and constrained unilaterally by an elastic obstacle ψ ∈ L2 (Ω), displacement function u can be obtained by solving the weak formulation: Find u ∈ V, such that a(u, v) + `(u, v) = ( f, v), ∀v ∈ V, (1)
Ω κ ( u − ψ )− vdxdy, t− = min{ t, 0}, ( f, v ) = Ω f vdxdy, ν ∈ (0, 1/2) is Poisson’s ratio and κ ≥ κ0 > 0 describes the stiffness of the obstacle. It was shown in [1] that the displacement function u can be derived by the minimization problem: Find u ∈ V, such that ∀v ∈ V J (u) ≤ J (v) with the total energy J (v) = 12 a(v, v) + 12 Ω κ [(v − ψ)− ]2 dxdy − ( f, v)
Summary
Let Ω ⊂ R2 be a bounded convex polygonal domain with a Lipschitz continuous boundary. ( Ω ) [21,22]; the lack of H 4 regularity makes it impossible to develop high accuracy instead of Hloc analysis It was shown in [10] that the solution is more regular if the obstacle is elastic. We attempt to present a high accuracy analysis of nonconforming double set parameter FEMs for the obstacle problem (2). Several nonconforming double set parameter plate elements have been successfully applied to deal with the two-sided displacement obstacle problem of the clamped plate [8], plate bending problems [16,27], the linear elasticity problem [28], the fourth-order elliptic singular perturbation problem [29,30,31] and so on. A non-C0 nonconforming double set parameter plate element is employed for the elastic obstacle problem (2). We carry out a numerical experiment to show the performance of the proposed method
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
