Product: ABAQUS/Standard
Some of the shell elements in ABAQUS/Standard (S4R5, S8R5, S9R5, and STRI65) use two variables at a node to define the change in the shell normal at the node, , during an increment. At some nodes in these elements and in other elements we use the three components of the rotation triplet as the rotation degrees of freedom. To provide inertia for all of these nodal variables, at a node N with two “rotation” variables we define
This expression neglects any rotation of the basis system that occurs during the increment. This is an approximation in large-displacement analysis: it is adopted for the sake of simplicity, based on the argument that we are not attempting to model the rotary inertia accurately.
At a node at which we use the three global rotation components we define
The first-order elements in ABAQUS use a lumped mass matrix. In this case is diagonal, so that the rotary inertia contribution at node N is
For a consistent mass element the rotary inertia contribution is
The time integration algorithms require initial conditions for each increment. For implicit integration these are the velocities and accelerations of the variables at the start of the increment, and .
At a node where three global rotation components are used, these initial values are directly available from the solution to the previous increment. At a node where only two variables define the rotation, we convert variables from the basis of one increment to that of the next through the approximation