Development Of New Hybrid Stress/Displacement-function Finite Element For Analyses Of Fracture And Mindlin-reisner Plate Problems

During past seventy years,the Finite Element Method has become one of the major numerical tools for simulations and analyses of science and engineering.However,the conventional Finite Element Method inevitably exists some insuperable shortcomings,such as the sensitivity problem to the mesh distortion and the low precision and efficiency problem for analysis of the field in which the stress exhibits dramatic changes.On the basis of high-performance hybrid stress/displacement-function method,this dissertation put forward some corresponding solutions to the above problems existing in plane crack,plate bending and plate crack simulations.The main contributions of this dissertation are as follows:Ⅰ.Based on the hybrid stress-function method,a new plane shape-free multi-node singular hybrid stress-function(HS-F)crack-tip element with drilling degrees of freedom,named by HSF-Crack-θ,is successfully constructed by employing the Williams basic analytical solution of the stress-function for plane crack problems in polar coordinates and the definition of Allman’s plane drilling degrees of freedom.The stress fields and the stress intensity factors(SIFs)in the vicinity of crack tip can be accurately simulated and captured while only a few elements are utilized.Then,a quasi-static 2D crack propagation modeling strategy is established by combination of the new singular element and a shapefree 4-node HS-F plane element with drilling degrees of freedom named HSF-Q4θ-7β proposed previously.Only a simple remeshing process with an unstructured mesh is needed for each simulation step.Numerical results show that the proposed scheme is an effective and low-cost technique for dealing with the crack propagation problems.Ⅱ.Based on the hybrid displacement-function method,a new scheme for constructing high-order and high-performance Mindlin-Reissner plate element is proposed by combining with the arbitrary order Timoshenko’s beam function.Meanwhile,three 8-node quadrilateral Mindlin-Reissner plate elements,HDF-P8-23β,HDF-P8-FREE and HDF-P8-SS1,are successfully formulated.Numerical results demonstrate that the proposed elements can eliminate the shear-locking phenomenon,exhibit excellent convergence and possess superior precision,and can still provide good and stable results even when extremely coarse and distorted meshes are used.For the edge effect problems,numerical results show that the combination of the new elements could accurately capture the peak value and the dramatic variations of resultants near the boundaries while only a few elements are utilized.Ⅲ.Based on the asymptotic expansion method and the hybrid displacementfunction method,the corresponding displacement fields,the related resultant fields and the stress intensity factors in the vicinity of the crack contained in the Mindlin-Reissner plate is derived,and the arbitrary multi-node high-order asymptotic displacement singular crack tip element named Asymptotic-Crack is formulated.And a high-order plate crack simulation scheme is also proposed by combining the new singular crack tip element and the 8-node quadrilateral Mindlin-Reissner plate element HDF-P8-23β proposed in this dissertation.Numerical results show that the proposed scheme could capture the stress intensity factor accurately even the mesh is sparse and distorted.Furthermore,the research on the size effect of the plate crack is also preliminarily realized.