TAILIEUCHUNG - Locking phenomena in finite element analysis of deep beam and removal method
Under certain material conditions, such elements may provide inaccurate results and exhibit slow convergence. Locking phenomena are the cause of these problems and this situation could limit the computation of many kinds of structures. This paper presents a deep beam element based upon mixed formulation, which may illuminate these locking phenomena. | Vietnam Journal of Mechanics, VAST, Vol. 27, No. 3 (2005), pp. 129 - 139 LOCKING PHENOMENA IN FINITE ELEMENT ANALYSIS OF DEEP REMOVAL METHOD NGUYEN THANG HOA , TRAN lCH TRINH MCMC Center, Hanoi University of Technology Abstract. Since earlier 30 years ago, Finite Element Methods (FEM) has become an indispensable tool of engineers for analysis mechanical behaviour of structures. Generally displacement models are used in most usual problems. Under certain material conditions, such elements may provide inaccurate results and exhibit slow convergence. Locking phenomena are the cause of these problems and this situation could limit the computation of many kinds of structures. This paper presents a deep beam element based upon mixed formulation, which may illuminate these locking phenomena. 1. INTRODUCTION Finite Element Methods is based upon the virtual work principle ("displacement models") [1] , it is easy for computation, however it may provide inaccurate results and exhibit slow convergence. This phenomenon is characterized by a severe underestimation of the displacements , . the structural response is too stiff. Since the late 1970s the term locking is employed. The locking phenomena have some types, volumetric locking occurs in modeling nearly incompressible and incompressible materials, shear locking in bending dominated problems . Thereto, there are some other types of locking, such as membrane locking, thickness locking, in the framework of the paper, these types of locking are not discussed. By the effect of locking phenomena, FEM may provide inaccurate results and exhibit slow convergence. Therefore, so many methods are used for locking removal. Selective Reduced Integration method (SRI) has also been proved effective in overcoming the locking, ., by Naylor [13], Hughes, Malkus and Hughes [11], and others. It may produce rank deficiency [1 2], leading to the so-called zero-energy modes and unstable solutions by many situations . The .
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