Theoretically, the constant stress patch test is not rigorous. Also, either the patch test of non-zero constant shear for Mindlin plate problem or non-zero strain gradient curvature of the microstructures can not be performed. To improve the theory of the patch test, a variational principle with relaxed continuity requirement of nonconforming element for inhomogeneous differential equations and the enhanced patch test condition and the individual element condition can be developed. The theory of the enhanced patch test proposed in this study can be applied to both homogeneous and inhomogeneous differential equations. Based on this theory, following objects can be achieved: 1) to establish a new type of elements to pass the patch test of the non-zero constant shear stress for Mindlin plate and the axisymmetric element satisfied the requirement of the C0-1 patch test of the non-zero constant curvature for the couple stress/strain gradient theory; 2) to study the problems of scale effect and strain localizition in the microstructures; 3)multi-scale analysis in the molecular dynamics-continuum mechanics.