• We performed a test of ADVENTURECluster Solver. The analysis model is a plate with a center circular hole. We use symmetry to model one-eighth of the plate bisecting along x, y and z-axes. Stress along the y-axis is applied uniformly. The fixed displacement boundary condition is applied to each section. MSC.Nastran is used for comparison. Analysis conditions are as follows:
  • Plate: 200�~200�~5mm
  • Radius of the hole of the plate: 25mm
  • Young's modulus: 200GPa
  • Poison ratio: 0.0
  • Displacement boundary condition: each of 3 sections is fixed
  • Tensile stress along the y-axis: 160MPa

  We show some results:

  • Theory
    
  • Comparison between the theory and the analysis by linear hexahedral elements
  • Static elastic analysis by linear tetrahedral elements
  • Static elastic-plastic analysis by linear tetrahedral elements

• Theory.
  This problem is represented as approximately infinite plate with a circular hole (radius a) where a uniform tensile stress along an axis applied.
  

  As in this figure, when the uniform tensile stress along the y-axis is applied, the stress distribution on the x-axis is given by

  

  which gives the maximum value at the intersection of the circle and the x-axis.

• Comparison between the theory and the analysis by linear hexahedral elements.
  Now we show a comparison of the theory, ADVENTURECluster and MSC.Nastran. The analysis was carried out under the following conditions:
  • Elements: Linear hexahedral elements
  • Number of elements: 9800
  • Number of nodes: 11715

  The results of ADVENTURECluster and MSC.Nastran almost nearly overlap each other. This is expected, because the analysis is static elastic. The difference between the theory and the two analysis results at x = 25 reflects the fact that the theory and analysis deal with an infinite and finite plate, respectively.

  

• Static elastic analysis by linear tetrahedral elements.
  The analysis by ADVENTURECluster and MSC.Nastran is carried out under the following conditions:
  • Elements: Linear tetrahedral elements
  • Number of elements: 44975
  • Number of nodes: 15280
  • Tensile stress: 160MPa

  Although it is natural because the analysis is static elastic, the two results almost completely coincide.

  	ADVENTURECluster	MSC.Nastran

• Static elastic-plastic analysis by linear tetrahedral elements.
  Static elastic-plastic analyses by linear tetrahedral elements are carried out. The following conditions are the same as the static elastic analysis by linear tetrahedral elements:
  • Elements: Linear tetrahedral elements
  • Number of elements: 44975
  • Number of nodes: 15280
  • Tensile stress: 160MPa

  In addition to these conditions, we assume

  • Material property: Bi-linear stress-strain curve is assumed
  • Yield function: von Mises yield function
  • Hardening rule: Isotropic
  • Initial yield stress: 200MPa
  • Gradient of work hardening: 2GPa

  As noted in Theory, since the stresses on the right edge of the hole along the x-axis is three times that of the applied stress, plastic flow appears in the vicinity of that point. In the following figures, denotes the equivalent plastic strain.

  	ADVENTURECluster	MSC.Nastran

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