ZHANG Can-hui, WANG Dong-dong, LI Tong-shan. Orthogonal Basic Deformation Mode Method for Zero-Energy Mode Suppression of Hybrid Stress Element[J]. Applied Mathematics and Mechanics, 2011, 32(1): 79-92. doi: 10.3879/j.issn.1000-0887.2011.01.009
 Citation: ZHANG Can-hui, WANG Dong-dong, LI Tong-shan. Orthogonal Basic Deformation Mode Method for Zero-Energy Mode Suppression of Hybrid Stress Element[J]. Applied Mathematics and Mechanics, 2011, 32(1): 79-92.

# Orthogonal Basic Deformation Mode Method for Zero-Energy Mode Suppression of Hybrid Stress Element

##### doi: 10.3879/j.issn.1000-0887.2011.01.009
• Rev Recd Date: 2010-11-30
• Publish Date: 2011-01-15
• A set of basic deformation modes for hybrid stress finite element were directly derived from the element displacement field.Subsequently by employing the so-called united orthogonal conditions a new orthogonalization method was also proposed.The resulting orthogonal basic deformation modes exhibit simple and clear physical meanings.In addition,they do not involve any material parameters and thus can be efficiently used to examine the element performance and serve as a unified tool to assess different hybrid elements.Therafter a convenient approach for identification of spurious zero-energy modes was presented through using the positive definiteness property of flexibility matrix.Moreover,based upon the orthogonality relationship between the given initial stress modes and the orthogonal basic deformation modes,an alternative method of assumed stress modes to formulate a hybrid element free of spurious modes was discussed.It was also found that the orthogonality of the basic deformation modes was the sufficient and necessary condition for suppression of spurious zero-energy modes.Numerical examples of 2D 4-node quadrilateral element and 3D 8-node hexahedral element were illustrated in details to demonstrate the efficacy of the proposed orthogonal basic deformation mode method.
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