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针对常应力分片检验理论上的不严格和不能做Mindlin板非零常剪力及细观应变梯度理论非零常应变梯度曲率分片检验的问题,基于对应齐次阶微分方程的放松连续条件的不协调元的变分原理,建立了通过分片检验的单体条件及被检验单元的收敛条件:除通过分片检验外,单元函数还应包含刚体位移和常应变模式,无伪零能模式和满足弱连续条件.建立了对应非齐次阶微分方程的放松连续条件的不协调元的变分原理和增强型分片检验条件及单体条件,通过增强型分片检验条件的单元的收敛条件是单元函数应包含刚体位移和满足平衡的非零应变模式,无伪零能模式和新的弱连续条件.提出的增强型分片检验条件是对齐次和非齐次阶微分方程的分片检验统一提法.对Mindlin板问题建立了非零常剪力分片检验,对细观偶应力-应变梯度理论问题建立了非零常应变梯度曲率C0?1分片检验.
Aiming at the problem that theory of normal stress slice test is not rigorous and can not do the test of nonzero constant strain gradient curvature of Mindlin plate with non-zero shear force and mesoscopic strain gradient theory, based on relaxation continuous condition of corresponding homogeneous order differential equation The principle of variational principle of disconforming elements is established, and the condition of passing the piece test and the condition of convergence of the unit to be tested are established. In addition to passing the piecewise test, the unit function should include the rigid body displacement and the normal strain mode. Mode and weak continuous conditions are established. The variational principle and enhanced fragmented verification conditions and the monomer conditions for the uncoordinated elements of the relaxed continuous condition are established for the corresponding nonhomogeneous differential equations. The convergence condition is that the unit function should include the rigid body displacement and the balanced non-zero strain mode, no pseudo-zero energy mode and a new weak continuous condition.The proposed enhanced sharpening test conditions are the points of homogeneous and inhomogeneous differential equations Piece test of uniform reference to establish a non-zero shear shear plate test of Mindlin plate problem, established a non-zero constant strain gradient C0? 1 on the mesoscopic even stress-strain gradient theory Test.