Abaqus/Explicit element loading verification

In this verification test all the available element types are tested by loading them with a gravity 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 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 = 7850.

A nonstructural mass contribution to the element mass is defined while the effective density is maintained at the above specified value by reducing the material density to the extent of the added nonstructural mass. Because the GRAV load is applied on both the structural mass and the nonstructural mass, the analytical solution used to verify the numerical results remains the same.

In the first step a gravity load is applied in the vertical direction (y-direction). The amplitude function for this gravity load is defined such that the load is ramped up to a value of 10 over the first half of the step and held constant over the second half of the step. In the second step the gravity load in the vertical direction is replaced with a gravity load in the horizontal direction (x-direction), which has an amplitude function that is similar to the vertical load.

In this verification test all the available element types are tested by loading them with a uniform 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 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 uniform 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 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 uniform 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 uniform 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 these verification tests all the available element types are tested by loading them with uniform pressure using distributed element-based loads and distributed surface loads. All the element nodes are fixed in position, and the reaction forces generated at the nodes are used to verify the load applications. Pipe elements (PIPE21 and PIPE31) are tested only with distributed element-based loads. Multiple steps are used to apply different loads. All the loads applied in previous steps are removed at the beginning of each step. Loads are linearly increased over the first half of each step and held constant over the second half.

Isotropic linearly elastic material is used for all elements. The material properties used are defined as follows: Young's modulus = 193.1 × 10⁹, Poisson's ratio = 0.3, and density = 785.

For beam (B21, B31) and pipe (PIPE21, PIPE31) elements in the case of element-based loads, uniform distributed force per unit length of 1.0 × 10⁵ is applied in along the x- and y-direction in the first and second steps, respectively. In the third step uniform distributed force per unit length of 1.0 × 10⁵ along the z-direction is applied on three-dimensional beam (B31) and pipe (PIPE31) elements.

For shell elements (S3R, S4R) and axisymmetric line elements (SAX1) uniform distributed normal force per unit area of 1.0 × 10⁵ is applied in the first step.

For three-edged planar elements (CPE3, CPE6M, CPS3, CPS6M) and axisymmetric elements (CAX3, CAX4R) a uniform distributed normal force per unit length of 1.0 × 10⁵ is applied on each element edge in the first three steps.

For four-edged planar elements (CPE4R, CPS4R) and axisymmetric elements (CAX4R) a uniform distributed normal force per unit length of 1.0 × 10⁵ is applied on each element edge in the first four steps.

For tetrahedral three-dimensional continuum elements (C3D4, C3D10, and C3D10M) a uniform distributed force per unit area of 1.0 × 10⁵ is applied on each face in the first four steps.

For prismatic three-dimensional continuum elements (C3D6) a uniform distributed force per unit area of 1.0 × 10⁵ is applied on each face in the first five steps.

For hexahedral three-dimensional continuum elements (C3D8) a uniform distributed force per unit area of 1.0 × 10⁵ is applied on each face in the first six steps.

In the case of surface-based loads, in the first step a uniform pressure of 1.0 × 10⁵ is applied on one of the element edge surfaces (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). In the second step the same uniform pressure is applied on other element edge surfaces or element faces.

In this verification test all the available element types are tested by loading them with a viscous pressure load. The nodes belonging to the plane strain, plane stress, and axisymmetric elements (CPE3, CPE4R, CPS3, CPS4R, CAX3, and CAX4R) are constrained in the x-direction; and an initial velocity of 100 is prescribed in the y-direction. The nodes belonging to the three-dimensional elements (C3D4, C3D6, and C3D8R) are constrained in the x- and z-directions, and an initial velocity of 100 is prescribed in the y-direction. The nodes belonging to the shell and membrane elements (S3R, S4R, M3D3, and M3D4R) are constrained in the x- and y-directions, and an initial velocity of 100 is prescribed in the z-direction. The nodes belonging to the axisymmetric shell element (SAX1) are constrained in the z-direction, and an initial velocity of 100 is prescribed in the r-direction.

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 = 7850. The coefficient of viscosity is 1000.

The viscous pressure load generates reaction forces at the nodes, which are used to verify the element load calculations. This test has only one step.

In this verification test all the available element types are tested by loading them with a viscous body or a stagnation load. The nodes belonging to the plane strain, plane stress, and axisymmetric elements (CPE3, CPE4R, CPS3, CPS4R, CAX3, and CAX4R) are constrained in the x-direction; and an initial velocity of 100 is prescribed in the y-direction. The nodes belonging to the three-dimensional elements (C3D4, C3D6, and C3D8R) are constrained in the x- and z-directions, and an initial velocity of 100 is prescribed in the y-direction. The nodes belonging to the shell and membrane elements (S3R, S4R, M3D3, and M3D4R) are constrained in the x- and y-directions, and an initial velocity of 100 is prescribed in the z-direction. The nodes belonging to the axisymmetric shell element (SAX1) are constrained in the z-direction, and an initial velocity of 100 is prescribed in the r-direction.

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 = 7850.

The viscous body and stagnation loads generate reaction forces at the nodes, which are used to verify the element load calculations.