Shell obstacle course: Pinched hemisphere
The linear static pinched hemisphere test considers a hemispherical shell loaded with opposing point loads along it's equator. Isotropic material properties are as per the figure below. Due to symmetry only a quarter of the shell is modeled.
Problem definition [2]
The key result is the X-displacement along one of the point loads, denoted by "u" in the following diagram, for which the reference value is "u_x" = 0.0924 [2].
The following X-displacement contour of the Kratos thin quad element (mesh = 285 elements) is provided for context.
Pinched hemisphere results: X-displacement contour of Kratos thin quad element
The results of the test for the thin and thick triangle Kratos shell elements are presented below.
Pinched hemisphere results: triangle elements
The results of the test for the thin and thick quadrilateral Kratos shell elements are presented below.
Pinched hemisphere results: quadrilateral elements
Both graphs above indicate all Kratos triangular and quadrilateral shell elements agree with the reference solution.
- Ted Belytschko et al. “Stress projection for membrane and shear locking in shell finite elements”. In: Computer Methods in Applied Mechanics and Engineering 51.1-3 (1985), pp. 221–258.
- Robin Bouclier, Thomas Elguedj, and Alain Combescure. “Efficient isogeometric NURBS-based solid-shell elements: Mixed formulation and method”. In: Computer Methods in Applied Mechanics and Engineering 267 (2013), pp. 86 –110.