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Problem definition

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].

Results

The following X-displacement contour of the Kratos thin quad element (mesh = 285 elements) is provided for context.

Pinched hemisphere displacement contour.

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.

References

  1. 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.
  2. 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.