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By introducing a new method to establish the local Cartesian coordinate system and calculate the derivatives of the shape functions with respect to the local coordinates,the membrane elements with vertex rigid rotational freedom called GQ12 and GQ12M based on this new method can achieve higher precision results than traditional methods.When applying this new method to the bilinear quadrilateral element Q4,the calculation accuracy is also improved.The numerical results demonstrate that GQ12 and GQ12M based on this new method can provide better membrane elements for flat shell elements.