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SUMMARYBased on a new generalized variational principle, a refined direct stiffness method (RDSM) which can be directly used to improve non-conforming elements is proposed. The formulation is similar to that of the direct stiffness method (DSM), but the constraint condition of interelement continuity is satisfied in an average sense and as a result convergence and high accuracy are insured. The well-known BCIZ nineparameter triangular thin plate bending element is refined by the RDSM to yield a new nine-parameter thin plate bending element RT9. Numerical examples are presented to show that the present model passes the patch test and possesses high accuracy.

SUMMARYBased on finite element formulations for the strain gradient theory of microstructures, a convergence criterion for the C 0-1 patch test is introduced, and a new approach to devise strain gradient finite elements that can pass the C 0-1 patch test is proposed. The displacement functions of several plane triangular elements, which satisfy the C 0 continuity and weak C 1 continuity conditions are evaluated by the C 0-1 patch test. The difference between the proposed C 0-1 patch test and the C 0 constant stress and C 1 constant curvature patch tests is elucidated.An 18-DOF plane strain gradient triangular element (RCT9+RT9), which passes the C 0-1 patch test and has no spurious zero energy modes, is proposed. Numerical examples are employed to examine the performance of the proposed element by carrying out the C 0-1 patch test and eigenvalue test. The proposed element is found to be without spurious zero energy modes, and it possesses higher accuracy compared with other strain gradient elements.

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