## 3.3. Coordinate Systems

The following coordinate system topics are available:

### 3.3.1. Understanding the Element Coordinate System

The element coordinate system is used for:

• Orthotropic material input

• Pressure loading input on certain faces of the surface effect elements

• Output of element quantities, such as stresses, strains, and thermal gradients

A default element coordinate system orientation is associated with each element type. In general, these systems are described below. Elements departing from this description have their default element coordinate system orientation described in Element Library.

Element coordinate systems are right-handed, orthogonal systems.

• Line elements

The default orientation is generally with the x-axis along the element I-J line.

• Solid elements

The default orientation is generally parallel to the global Cartesian coordinate system.

If the program generates SOLID185 or SOLID186 elements during a 2-D to 3-D analysis (MAP2DTO3D and EEXTRUDE), the element coordinate system's third direction is in the hoop direction about the global Y axis (axisymmetric cases) or in the global Z direction (plane strain cases). For more information, see 2-D to 3-D Analysis in the Mechanical APDL Advanced Analysis Guide.

• General axisymmetric elements

The general orientation for SOLID272 and SOLID273 elements is determined by the cylindrical coordinate system, with z and the origin defined via SECTYPE and SECDATA commands, and θ = 0 on the master plane; the r, θ, and z directions adhere to the right-hand rule. For more information, see General Axisymmetric Elements.

• Shell elements

The default orientation for current-technology elements SHELL131, SHELL132, SHELL181, SOLSH190, and SHELL281 has the S1 (shell surface coordinate) axis aligned with the first parametric direction of the element at the center of the element. For elements with edges IJ and KL parallel (rectangular or trapezoidal elements), the default orientation (S1 axis) can be interpreted as being parallel to edge IJ (as used by legacy elements such as SHELL63).

#### 3.3.1.1. Modifying the Element Orientation

Unless otherwise changed, the element coordinate system orientation is the default orientation for that element type. The orientation may be changed for area and volume elements by making it parallel to a previously defined local system (ESYS) or, for some elements, by a KEYOPT selection. If both are specified, the ESYS definition overrides.

The coordinate systems of axisymmetric elements may only be rotated about the global Z axis; however, general axisymmetric elements can be rotated about any axis.

Shell elements For shell elements, the ESYS orientation uses the projection of the local system on the shell surface. The element x-axis is determined from the projection of the local x-axis on the shell surface. If the projection is a point (or the angle between the local x-axis and the normal to the shell is 0° (plus a tolerance of 45°)), the local y-axis projection is used for the element x-axis direction. The z and y-axes are determined as described for the default orientation.

For non-midside-node shell elements, the projection is evaluated at the element centroid and is assumed constant in direction throughout the element. For midside-node shell elements, the projection is evaluated at each integration point and may vary in direction throughout the element.

Axisymmetric elements For axisymmetric elements, only rotations in the X-Y plane are valid. Some elements also allow element coordinate system orientations to be defined by user written subroutines. (See the Guide to User-Programmable Features in the Mechanical APDL Programmer's Reference.)

Layered elements Layered elements use the x-axis of the element coordinate system as a base from which to rotate each layer to the layer coordinate system. The layers are rotated by the angles input on the SECDATA or RMORE commands. Material properties, stresses, and strains for layered elements are based on the layer coordinate system, not the element coordinate system.

All element coordinate systems shown in the element figures assume that no ESYS orientation is specified.

The orientation of output element quantities can be adjusted. See Rotating Results to a Different Coordinate System in the Mechanical APDL Basic Analysis Guide.

Element coordinate systems can be displayed as a triad with the /PSYMB command or as an ESYS number (if specified) with the /PNUM command. Triad displays do not include the effects of any real constant angle.

For large-deflection analyses, the element coordinate system rotates from the initial orientation described above by the amount of rigid body rotation of the element.

2-D and axisymmetric elements operate in the global Cartesian X-Y plane. Accordingly, rotations of the element coordinate system (and/or the coordinate system of any node used by the element) can occur in the X-Y plane only. For example, if a Y-Z rotation is input for such an element, the program issues an error message.

### 3.3.2. Elements That Operate in the Nodal Coordinate System

A few special elements operate solely within the nodal coordinate system:

 COMBIN14 Spring-Damper with KEYOPT(2) = 1, 2, 3, 4, 5, or 6 MATRIX27 Stiffness, Damping, or Mass Matrix COMBIN37 Control Element FLUID38 Dynamic Fluid Coupling COMBIN39 Nonlinear Spring with KEYOPT(4) = 0 COMBIN40 Combination Element TRANS126 Electromechanical Transducer COMBI214 2-D Spring-Damper Bearing

These elements, defined in the nodal coordinate system, allow for easy directional control, especially for the case of two-node elements with coincident nodes.

If UX, UY, or UZ degrees of freedom are being used, the nodes are not coincident, and the load is not acting parallel to the line connecting the two nodes, there is no mechanism for the element to transfer the resulting moment load, resulting in loss of moment equilibrium. The sole exception is MATRIX27, which can include moment coupling when appropriate additional terms are added to the matrix.

You cannot sum nodal force and moment contributions (FSUM) for these elements if the 1-D option is activated and nodes are rotated (NROTAT).

If any of the nodes have been rotated (NROTAT), consider the following:

• If the nodes of elements containing more than one node are not rotated in precisely the same way, force equilibrium may not be maintained.

• Accelerations operate normally in the global Cartesian system. Because no transformation is done between the nodal and global systems, however, the accelerations effectively act on any element mass in the nodal system, giving unexpected results. It is therefore good practice not to apply accelerations when these elements use rotated nodes.

• Mass and inertia relief calculations will not be correct.

### 3.3.3. Solution Coordinate Systems

For homogeneous elements, element solution coordinate systems are generally identical to the nodal or the element coordinate systems adopted by the elements.

For composite elements, solution coordinate systems can be independently defined for different components, such as layers in a layered-shell element (SHELL181) and fibers in a discrete reinforcing element (REINF264). The solution coordinate systems in composite elements are also called layered coordinate systems, and are specifically identified via the RSYS,LSYS command.

For more information, see Rotating Results to a Different Coordinate System in the Mechanical APDL Basic Analysis Guide.