Elastostatic

• The solution technique could be Direct BEM (DBEM) or Indirect BEM (IBEM)
• The body could be made of isotropic or orthotropic material.
• The body could be made from multiple materials with forces specified at the interfaces if needed.
• Forces could be specified at a point, on a line or over the enire body.
• For isotropic material moments could be specified at a point or on a line.
• Boundary conditions could be on traction, displacement or mixed. Spring type and friction (all slip) will be permitted in the near future.
• For isotropic material the integral equations in the Indirect method could be formulated using point force or point displacements.

Numerical Examples

• Disc Under Bi-axial tension

  Reference: M.Vable and B. Ammons (1995) "A study of the Direct and Indirect BEM" 17th Boundary Element International conference. Madison Wisconsin July 17-19,

  The two integral operators in the Direct BEM appear individually in two different formulations of the Indirect BEM. The two Indirect BEM correspond to constructing the integral equations using force singularity and constructing the integral equations using displacement singularities.

  Results show:

  • Solution by Direct BEM is between the two indirect BEM.
  • There is a spike at each element end if the order of singularity is two and linear lagrange polynomials (non-conforming) are used for approximating the unknowns. This is seen direct BEM and indirect BEM with displacement discontiniuity..
  • The effect of spike propogates inward and though the error decreases it reaches some limiting value that is dependended on the spike magninude.
  • The use of Cubic Hermite polynomials (conforming element) removes the spike and the accuracy for integral operators with 2nd order singularity improves by several orders of magnitude.

Move to

Fracture Mechanics

Poisson's Equation

Plate Bending

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