精化直接刚度法及九参数三角形薄板单元

Refines direct stiffness method and refined nine parameters triangular thin bending elements

提出一种可直接用于精化不协调元的精化直接刚度法．其列式与直接刚度法类同，单元间的协调条件平均满足；既能保证收敛又能提高精度．精化直接刚度法的变分根据是广义变分原理．用精化直接刚度法对著名的九参数三角形Ｚｉｅｎｋｉｅｗｉｃｚ薄板单元进行了精化，建立了新的九参数三角形板元ＲＴ9和ＲＴ１０．数值结果表明本文建立的单元收敛且精度高．

A refined direct stiffness method which can be directly used to refine non-conforming elements is proposed, whose formulation is as similar to that of the direct stiffness method. The constraint coondition of inter element continuity is satisfied in an average sense therefore the convergence and high accuracy are insured. The basis of the generalized variational principle of this method is found. The well-known Zienkiewicz's 9-parameter triangular thin bending element is refined by using the refined direct stiffness method, and new 9-parameter triangular thin bending elemnets RT9 and RT10 are developed. The numerical examples show that the present models insure convergence and have high accuracy.