FINITE ELEMENTS OF THE PLANE PROBLEM OF THE THEORY OF ELASTICITY WITH DRILLING DEGREES OF FREEDOM

Twelve new finite elements with drilling degrees of freedom have been developed: triangular and quadrangular elements based on a modified hypothesis about the value of approximating functions on the sides of the element, which made it possible to avoid dimensional instability when all rotation angles are zero; incompatible and compatible triangular and quadrangular elements which can have additional nodes on the sides. Approximating functions satisfy the following condition: the value of the rotational degree of freedom of a node is nonzero and equal to one only for one of them. Numerical examples illustrate estimated minimum orders of convergence for displacements and stresses. All created elements retain the existing symmetry of the design models.

Quasi-Static Crack Propagation Modeling Using Shape-Free Hybrid Stress-Function Elements with Drilling Degrees of Freedom

A new plane shape-free multi-node singular hybrid stress-function (HS-F) element with drilling degrees of freedom, which can accurately capture the stress intensity factors at the crack tips, is developed. Then, a quasi-static 2D crack propagation modeling strategy is established by combination of the new singular element and a shape-free 4-node HS-F plane element with drilling degrees of freedom proposed recently. Only simple remeshing with an unstructured mesh is needed for each simulation step. Numerical results show that the proposed scheme is an effective and robust technique for dealing with the crack propagation problems.