On The Plane Elasticity Problem Locking-free Finite Element Method Convergence

The theme of this dissertation is using nonconforming finite element methods to avoid Locking phenomenon in planar elasticity problem, a such rectangle element is given.The key to the problem is the construction of the operator for the planar elasticity: γ_T: L~2(T)â†'ω_h, γ_Tω= 1/(|T|) t ωdxdy, P_Fω = 1/(|F|) F ωds, here the finite element spaces in the rectangle element can satisfies the regularity of operator mentioned above. The key to the step is the proof of the discrete version of Korn' second inequality in the nonconforming finite element spaces for the planar elasticity with pure traction boundary condition, here a new nonconforming finite element method was proposed, then, the uniform convergence of the element is proved, and an optimal estimate is given.