VDLOAD: nonuniform loads

In this verification test all the available element types are tested by loading them with a nonuniform body force. All the element nodes are fixed in position, and the reaction forces generated at the nodes are used to verify the element load calculations. The purpose of this test is to verify the element load calculations, not to test all the capabilities of user subroutine VDLOAD.

The material model is isotropic linear elasticity. The material properties used are defined as follows: Young's modulus = 193.1 × 10⁹, Poisson's ratio = 0.3, and density = 785.

In the first step a nonuniform body force of 1.0 × 10⁵ is applied in the x-direction for all the elements except the axisymmetric elements, where it is applied in the r-direction. The amplitude function for this nonuniform body force is defined such that the load is ramped on over the first half of the step and held constant for the rest of the analysis. In the second step another nonuniform body force of 1.0 × 10⁵ is applied in the y-direction for all the elements except the axisymmetric elements, where it is applied in the z-direction. This load is applied using the same amplitude function that was used in the first step. For C3D4, C3D6, C3D8R, S3R, S4R, M3D3, and M3D4R elements, another nonuniform body force of 1.0 × 10⁵ is applied in the z-direction in a third step. This load also has the same amplitude function that was used in the first step.

In this verification test all the available element types are tested by loading them with a nonuniform pressure load. All the element nodes are fixed in position, and the reaction forces generated at the nodes are used to verify the element load calculations. The purpose of this test is to verify the element load calculations, not to test all the capabilities of user subroutine VDLOAD.

The material model is isotropic linear elasticity. The material properties used are defined as follows: Young's modulus = 193.1 × 10⁹, Poisson's ratio = 0.3, and density = 785.

In the first step a nonuniform pressure of 1.0 × 10⁵ is applied on element edges (for CPE3, CPE4R, CPS3, CPS4R, CAX3, CAX4R, SAX1, R2D2, and RAX2 elements) or element faces (for C3D4, C3D6, C3D8R, S3R, S4R, M3D3, M3D4R, R3D3, and R3D4 elements). For the beam and pipe elements (B21, B31, PIPE21, and PIPE31) a nonuniform force per unit length of 1.0 × 10⁵ is applied in the y-direction. The amplitude function for this nonuniform pressure load is defined such that the load is ramped on over the first half of the step and held constant for the rest of the analysis. In the second step a nonuniform pressure of 1.0 × 10⁵ is applied on a different element edge (for CPE3, CPE4R, CPS3, CPS4R, CAX3, and CAX4R elements) or element face (for C3D4, C3D6, and C3D8R elements). For the beam elements (B21 and B31) a nonuniform force per unit length of 1.0 × 10⁵ is applied in the x-direction. These loads are applied using the same amplitude function that was used in the first step.