The spring element method (SEM) is a numerical method that uses a spring system to describe an element. Different elements can be described as different spring systems; and the definition of the spring stiffness expressions in the systems is the key point of the spring element method. The four-node rectangular element is described by 6 basic springs
each of which contains two derived springs: normal spring and tangential spring. Poisson spring and pure shear spring are used to describe Poisson and shear effects of the element. Thus a four-node rectangular spring element is presented. Compared with the element stiffness matrix of finite element method
the stiffness expression of each spring is obtained. Springs of the same kind have the same expressions. The stiffness expressions of the normal and tangential springs have corresponding coefficients to be decided. By varying the coefficients in the stiffness expressions of springs
expressions of constant strain
bilinear or Wilson incompatible finite element are achieved by this element. The accuracy of the SEM is verified by theoretical derivation; and this method is applied to the continuum-based discrete element method (CDEM) for case verification. The features of the four-node rectangular spring element are as follows. Different accuracies can be found in different elements. This element can significantly improve the accuracy of the bending problem of beam. Elements with different accuracies can be achieved by using different coefficients.
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Related Author
ZHANG Qing-bo
FENG Chun
WANG Jie
JIANG Wei
ZHENG Hong
WU Ai-qing
FENG Xi-xia
LU Bo
Related Institution
State Key Laboratory of Geomechanics and Geotechnical Engineering, Institute of Rock and Soil Mechanics, Chinese Academy of Sciences
Center of Discontinuous Deformation Analysis, Key Laboratory of Geotechnical Mechanics and Engineering of the Ministry of Water Resources, Yangtze River Scientific Research Institute
College of Airport Engineering, Civil Aviation University of China
Tianjin Municipal Engineering Design and Research Institute
MOE Key Laboratory of Coast Civil Structure Safety, Tianjin University