TRANS126 Element Description

TRANS126 represents a transducer element that converts energy from an electrostatic domain into a structural domain (and vice versa), while also allowing for energy storage. The element fully couples the electromechanical domains and represents a reduced-order model suitable for use in structural finite element analysis as well as electromechanical circuit simulation. The element has up to two degrees of freedom at each node: translation in the nodal x, y, or z direction and electric potential (VOLT). The element is suitable for simulating the electromechanical response of micro-electromechanical devices (MEMS) such as electrostatic comb drives, capacitive transducers, and RF switches for example.

The characteristics of the element are derived from electrostatic field simulations of the electromechanical device using the electrostatic elements PLANE121, SOLID122, and SOLID123, as well as the CMATRIX macro. The TRANS126 element represents the capacitive response of the device to motion in one direction. Running a series of electrostatic simulations and extracting capacitance (CMATRIX command) as a function of stroke (or deflection) provides the necessary input for this element. The capacitance versus stroke represents a "reduced-order" characterization of the device suitable for simulation in this transducer element. Up to three characterizations (in X, Y, or Z) can be made from sets of electrostatic simulations to create three independent transducer elements to characterize a full translational response of the device. See TRANS126 in the Mechanical APDL Theory Reference for more details about this element.

Figure 126.1: TRANS126 Geometry

TRANS126 Input Data

The geometry, node locations, and the coordinate system for this element are shown in Figure 126.1: TRANS126 Geometry. Nodes I and J define the element. The nodes need not be coincident. The element may lie along any one of the three global Cartesian axes as shown in Figure 126.1: TRANS126 Geometry, or it may exist in any arbitrary coordinate system as long as the nodes are rotated into the arbitrary coordinate system in such a manner that one of the axes lies along the element's I-J direction. Use the degree of freedom option (KEYOPT(2)) to select the appropriate structural displacement degree of freedom (corresponding to the element's I-J direction) and electric potential. Orientation of the element with respect to nodal displacements (node J relative to node I) is critical. Orient the element such that a positive movement of node J relative to node I produces a positive displacement (see Figure 126.1: TRANS126 Geometry). Figure 126.4: TRANS126 Valid/Invalid Orientations illustrates valid and invalid orientations of the element for a UX-VOLT degree of freedom set.

The capacitance vs. stroke data for the element is entered through the real constant table. Use KEYOPT(3) to select from two different methods of input. For KEYOPT(3) = 0, the real constant data (R7-R11) represent the coefficients of an equation (see Figure 126.2: TRANS126 Capacitance Relationship). Use as many terms as are required to represent the curve. For KEYOPT(3) = 1, the real constant data (R7-R46) represent discrete pairs of capacitance and stroke data. Up to 20 pairs of data may be input. The minimum required is 5 data point sets. A curve is fit to the discrete data sets represented by the equation shown in Figure 126.2: TRANS126 Capacitance Relationship.

Figure 126.2: TRANS126 Capacitance Relationship

The initial gap distance GAP (R3) represents the initial distance between conducting walls of the electromechanical device (that is, plates of a parallel capacitor, beams of a comb drive, etc.). The initial gap value should fall within the range of the capacitance vs. stroke data as shown in Figure 126.2: TRANS126 Capacitance Relationship. The minimum gap distance GAPMIN (R4) represents the physical location where the gap is closed. If the gap closes to GAPMIN, the element behaves like a contact element with a normal stiffness KN represented by real constant R5. GAP and GAPMIN default to near-zero if not defined. Figure 126.3: TRANS126 Force Relationship illustrates the force vs. stroke for the transducer element. The curve highlights the capacitive force (which is compressive and acts to close the gap), and the contact force (which restrains the motion once the gap reaches GAPMIN). KN defaults to a stiffness represented by the slope from the capacitive force at GAPMIN to the origin as shown in Figure 126.3: TRANS126 Force Relationship.

Figure 126.3: TRANS126 Force Relationship

The element supports nodal voltage and displacements (D) as well as nodal current and force (F). Use IC to input an initial starting value of voltage or displacement for a transient analysis, or an initial guess for a static analysis.

The element supports static, transient, prestressed harmonic, and prestressed modal analyses. The element is nonlinear for static and transient analyses and requires an iterative solution to converge. The element produces an unsymmetric matrix.

Prestress effects are automatically included in a linear perturbation harmonic analysis or a linear perturbation modal analysis (for example, a base static analysis with an applied DC voltage followed by a linear perturbation harmonic analysis with an applied AC voltage). Alternatively, prestress effects can be activated via the PSTRES command.

The transducer element by nature has both stable and unstable solutions. If the system stiffness is negative, convergence problems can occur near unstable solutions. This typically occurs at small gap distances near GAPMIN. Use KEYOPT(6) = 1 to select the augmented stiffness method if you encounter convergence problems. In this method, the electrostatic stiffness is set to zero to guarantee a positive system stiffness. After convergence is reached, the electrostatic stiffness is automatically reestablished for postprocessing and subsequent analyses.

The next table summarizes the element input. Element Input gives a general description of element input.

TRANS126 Output Data

The solution output associated with the element is shown in Table 126.2: TRANS126 Element Output Definitions.

The element output directions are parallel to the element coordinate system. A general description of solution output is given in Solution Output in the Element Reference. See the Basic Analysis Guide for ways to view results.

If this element is used in a harmonic analysis, all variables will be stored in two-column arrays as complex variables. The first column will be titled real component and the second column will be titled imaginary component. If the variable is not complex, the same value will be stored in both columns.

The Element Output Definitions table uses the following notation:

A colon (:) in the Name column indicates that the item can be accessed by the Component Name method (ETABLE, ESOL). The O column indicates the availability of the items in the file jobname.out. The R column indicates the availability of the items in the results file.

In either the O or R columns, “Y” indicates that the item is always available, a letter or number refers to a table footnote that describes when the item is conditionally available, and “-” indicates that the item is not available.

Table 126.3: TRANS126 Item and Sequence Numbers lists output available through ETABLE using the Sequence Number method. See Element Table for Variables Identified By Sequence Number in the Basic Analysis Guide and The Item and Sequence Number Table in this reference for more information. The following notation is used in Table 126.3: TRANS126 Item and Sequence Numbers:

TRANS126 Assumptions and Restrictions

Figure 126.4: TRANS126 Valid/Invalid Orientations

TRANS126 Product Restrictions

There are no product-specific restrictions for this element.