1.3.3 Three-dimensional solid elements

Product: ABAQUS/Standard

Elements tested

C3D4 C3D4H C3D6 C3D6H C3D8 C3D8H C3D8I C3D8IH C3D8R C3D8RH C3D10 C3D10H C3D10M C3D10MH C3D15 C3D15H C3D15V C3D15VH C3D20 C3D20H C3D20R C3D20RH C3D27 C3D27H C3D27R C3D27RH

Problem description

Material:

Linear elastic, Young's modulus = 30 × 10⁶, Poisson's ratio = 0.3.

Boundary conditions:

= = = 0, = 0, = 0, = 0.

Step 1

A distributed pressure of 1000/area is applied on each face, and equivalent concentrated forces for shear loading, defined such that all three shear stresses are of magnitude –1000.

Response:

Stresses

–1000 at every integration point.

Strains

–1.3333 × 10^–5, –8.6667 × 10^–5.

Displacements

For lower-order elements the test description is complete. For higher-order elements another step definition is included.

Step 2

Hydrostatic pressure loading is applied to the four vertical faces, varying from 0 at top to 1000/area at bottom, in addition to the Step 1 loads.

Response:

Stresses

–1000(2 – z), –1000, –1000.

Strains

3.333 × 10^–5(0.7z – 1.1), 3.333 × 10^–5(0.2 – 0.6z),

–8.66667 × 10^–5.

Results and discussion

Elements using reduced integration may have additional boundary conditions to those specified above.

Elements C3D27R and C3D27RH employ 21 nodes in this test to produce the exact solutions. The lack of midface nodes is consistent with the elements' intended use, since no contact elements are present.

All elements except C3D20RH yield exact solutions. The stresses calculated for this element are correct.

The *SECTION FILE and *SECTION PRINT output requests are used in some of the input files to output accumulated quantities on the face in the y-z plane. The area of the face is 2.0 in both steps. The accumulated force is reported in a coordinate system that is local to the section. In Step 1 the force is 2000 in each local direction. In Step 2 the total force component in the local 1-direction (normal to the face) changes to 3000.