Boundary Conditions and Loads¶

In FrontISTR, boundary conditions and loads for structural, heat conduction, and dynamic analyses are defined with keywords. In static structural analysis, the defined boundary conditions and loads are grouped by group ID and activated for each step through !STEP using its BOUNDARY or LOAD line. In dynamic analysis as well, !BOUNDARY, !CLOAD, !VELOCITY, !ACCELERATION, and !SPRING for the implicit method can be activated by group from !STEP. Conditions that vary with time are scaled using !AMPLITUDE, and linear relationships among multiple degrees of freedom are defined with !EQUATION.

Overview¶

Boundary conditions and loads can be classified by analysis type as follows.

Analysis Type	Main Keywords	Purpose
Structural analysis	`!BOUNDARY`	Applies fixed constraints, prescribed displacements, and prescribed rotation about a rotation center.
Structural analysis	`!CLOAD`	Applies concentrated nodal forces, moments on rotational degrees of freedom, and torque about a rotation center.
Structural analysis	`!DLOAD`	Applies surface pressure, surface loads, body forces, gravity, and centrifugal force.
Structural analysis	`!SPRING`	Applies spring supports to nodal degrees of freedom.
Structural analysis	`!TEMPERATURE`	Directly specifies nodal temperatures used in thermal stress analysis or reads them from a result file.
Dynamic analysis	`!VELOCITY`, `!ACCELERATION`	Applies initial velocity or acceleration, or time-varying prescribed velocity or acceleration.
Heat conduction analysis	`!FIXTEMP`, `!CFLUX`, `!DFLUX`, `!SFLUX`, `!FILM`, `!SFILM`, `!RADIATE`, `!SRADIATE`	Applies fixed temperature, heat flux, convection, and radiation.
Common	`!AMPLITUDE`	Specifies time-varying scale factors for boundary conditions and loads in tabular form.
Mesh definition	`!EQUATION`	Defines multi-point constraint equations.

In structural analysis, degree-of-freedom numbers 1, 2, and 3 are normally treated as translational degrees of freedom, and 4, 5, and 6 as rotational degrees of freedom. Rotational degrees of freedom are meaningful in models with six degrees of freedom, such as shell and beam elements. For models containing only two- or three-dimensional solid elements, specify constraints and loads only within the range of degrees of freedom possessed by the target nodes.

Displacement Constraints in Structural Analysis¶

Displacement constraints are specified with !BOUNDARY. A range of degrees of freedom and a value are given for a node or node group. A value of 0 defines a fixed constraint, while a nonzero value defines a prescribed displacement or prescribed rotation.

In structural analysis, !BOUNDARY accepts a degree-of-freedom range from 1 through 6. 1 through 3 correspond to translational displacement, while 4 through 6 correspond to rotational constraints at nodes that have rotational degrees of freedom. Because a range of degrees of freedom can be specified together, for example, translation can be constrained by fixing 1 through 3 simultaneously.

When the AMP parameter is specified, the prescribed value varies with time according to an amplitude function. With the normal specification, prescribed displacement is applied incrementally according to the load factor within the step or the change in the amplitude function. When TOTAL=YES is specified, the specified value is treated as the target total displacement.

When ROT_CENTER is specified, a rotational constraint can be applied with respect to a center node group. With this specification, translational displacements of the target node group are calculated from the amount of rotation and imposed as constraints. The combination of ROT_CENTER and TOTAL=YES is not supported, so rotational constraints about a rotation center are used as incremental specifications.

Concentrated Loads in Structural Analysis¶

Concentrated nodal loads are specified with !CLOAD. When a node or node group, degree-of-freedom number, and load value are given, the load is incorporated into the right-hand side for that degree of freedom.

Values specified for translational degrees of freedom 1 through 3 are treated as nodal forces in the coordinate directions. In models with rotational degrees of freedom, values specified for 4 through 6 can apply moments to the rotational degrees of freedom. When the AMP parameter is specified, the concentrated load is multiplied by the value of the amplitude function.

When ROT_CENTER is specified, the load is applied as torque about the center node group. In this case, the specified torque vector is distributed to nodal forces based on the position vectors from the center to the target nodes. Because torque cannot be distributed when the center and a target node are at the same position, the geometric relationship between the rotation center and the load points must be checked.

Care is required when !CLOAD is specified for a node group in a model that also uses !MESH with REFINE (mesh refinement, Refiner). Refinement creates new midside nodes on edges contained in the original node group, and these midside nodes are also added to the same node group. Because !CLOAD assigns the same concentrated-load value to every node in the node group, the same concentrated load is also applied to the added midside nodes, resulting in a total load different from that intended before refinement. When specifying concentrated loads by node group, account for the increase in load points caused by refinement, or preferably specify individual nodes directly. If !CLOAD is specified for a node group containing two or more nodes in the refined mesh, a warning showing the group name and the post-refinement node count is output when the control data are read. The analysis continues.

Distributed Loads and Body Forces in Structural Analysis¶

Distributed loads and body forces are specified with !DLOAD. !DLOAD specifies a load type and parameters for an element group or surface group. Time variation is specified with the AMP parameter.

The main load types are as follows.

Load Type	Description
`P0`, `PP`, `P1`–`P6`	Applies pressure acting on an element face. The correspondence between face numbers and element faces depends on the element type.
`PX`, `PY`, `PZ`	Specifies pressure with an explicit coordinate direction. It is converted to a direction vector during input processing.
`S...`	Applies a surface load to a surface group. The face number is obtained from the surface-group definition.
`BX`, `BY`, `BZ`	Applies a body force in a coordinate direction.
`GRAV`	Specifies the gravitational acceleration vector. It is combined with material density and incorporated as a body force.
`CENT`	Applies centrifugal force based on a rotation axis and angular velocity.

When FOLLOW=YES is specified, surface pressure follows the orientation of the deformed surface. This specification is meaningful in structural analysis that accounts for finite deformation. In analyses where nonlinear geometry is disabled, follower pressure is disabled by the implementation.

As with P1 through P6 and S1 through S6 on the heat-analysis side, the meaning of face numbers differs by element type. See the keyword reference for the specific correspondence of face numbers and the order of data fields.

Spring Supports in Structural Analysis¶

Spring supports are specified with !SPRING. When a node or node group, degree-of-freedom number, and spring constant are given, the spring stiffness is added to the diagonal stiffness of the target degree of freedom, and the spring reaction force is incorporated into the right-hand side as an internal force.

When specified for degrees of freedom 1 through 3, the support is treated as a translational spring. In models with rotational degrees of freedom, specifying 4 through 6 allows rotational springs to be used. Check the degree-of-freedom configuration so that springs are not assigned to degrees of freedom absent from the target model.

The displacement reference resisted by the spring is selected with the INCREMENTAL parameter. With the default INCREMENTAL=NO, a spring reaction force proportional to the cumulative displacement from the start of the analysis is incorporated. In other words, the internal force is the product of the spring constant and the cumulative displacement. With INCREMENTAL=YES, the spring reference position is reset for each increment to the converged state of the preceding increment, and a spring reaction force proportional only to the displacement increment within that increment is incorporated. In other words, the internal force is the product of the spring constant and the displacement increment within that increment, and displacement carried across increments does not contribute to the spring reaction force.

Time variation of the spring constant is specified with the AMP parameter. When an amplitude function name is specified, the spring constant is multiplied by the value of the amplitude function. The amplitude value is evaluated at the end time of the current increment, allowing supports that engage or release partway through a step to be represented. If AMP is not specified, the spring constant is not varied over time by an amplitude function.

Both INCREMENTAL and AMP are effective in static analysis and implicit dynamic analysis. To switch the spring support itself on or off for each step, use the group ID and !STEP with its LOAD specification.

Temperature Loads in Structural Analysis¶

Use !TEMPERATURE to apply loads due to thermal strain in structural analysis. When a temperature is specified for each node or node group, equivalent nodal forces for thermal stress analysis are assembled based on the difference from the reference temperature or the previous temperature. The coefficient of thermal expansion is specified in the material definition. The reference temperature is specified with !REFTEMP.

Temperature can either be specified directly in the control file or read from a result file produced by heat conduction analysis or another analysis. When READRESULT is specified, nodal temperatures on the data lines are not read; instead, result data specified by SSTEP, INTERVAL, READTYPE, and related parameters are read. When using a result file, its saved time or step number must correspond to the specification on the structural-analysis side.

Because !TEMPERATURE has no AMP parameter, it is not subject to scaling by an amplitude function. To vary the temperature history, control the temperature data themselves, the heat-analysis results being read, or the step subdivision.

Initial Conditions and Prescribed Values in Dynamic Analysis (Velocity and Acceleration)¶

In dynamic analysis, !VELOCITY and !ACCELERATION can specify initial conditions or prescribed values for velocity or acceleration. Both specify a node or node group, a degree-of-freedom range, and a value. The degree-of-freedom range is 1 through 6; in models with rotational degrees of freedom, 4 through 6 correspond to angular velocity or angular acceleration.

TYPE=INITIAL specifies the initial velocity or initial acceleration at the start of the analysis. When an initial velocity is given, the initial acceleration is calculated for consistency with the equation of motion. When an initial acceleration is given, there is a path in which the initial velocity is calculated.

TYPE=TRANSIT specifies a time-varying prescribed velocity or prescribed acceleration. If TYPE is omitted, it is treated as TRANSIT. When AMP is specified, the amplitude function is interpolated at the dynamic-analysis time and multiplied into the prescribed value.

Excitation Forces in Frequency Response Analysis¶

Excitation forces for frequency response analysis are specified with !FLOAD. Specify a node, node group, or surface group together with a degree-of-freedom number and value. The specified value is treated as an excitation force in the corresponding coordinate direction; time-variation specifications used with !CLOAD or !DLOAD (AMP) are not used.

The complex amplitude of harmonic excitation is specified separately for the real and imaginary parts with the LOAD CASE parameter. Writing two cards for the same target, one with LOAD CASE=1 and one with LOAD CASE=2, makes it possible to represent phase-shifted excitation.

The dimensions of the value depend on the specified target. For a node number or node group name, the value is a concentrated force; for a surface group name, it is a surface force per unit area. When a surface group is specified, the force is integrated over the surface and distributed as equivalent nodal forces, as with surface pressure in !DLOAD. Unlike pressure, however, the direction is the coordinate direction corresponding to the specified degree-of-freedom number rather than the surface normal.

Multi-Point Constraints¶

Use the multi-point constraint function when a linear relationship must be imposed among multiple nodal degrees of freedom. The corresponding keyword is !EQUATION, which can express relationships such as rigid coupling, periodic boundaries, and displacement relationships between nodes that are difficult to represent with a fixed constraint on a single node and a single degree of freedom.

For guidance on using multi-point constraints, how they are handled by the linear solver, and their relationship to other degree-of-freedom coupling functions such as contact TIED, see Multi-Point Constraints.

Boundary Conditions in Heat Conduction Analysis¶

In heat conduction analysis, fixed temperature, heat flux, convection, and radiation are applied as boundary conditions. Separately from !STEP for structural analysis, time control for heat analysis is specified with !HEAT.

Keyword	Target	Description	Amplitude Specification
`!FIXTEMP`	Node or node group	Fixes temperature.	`AMP`
`!CFLUX`	Node or node group	Applies concentrated nodal heat flux.	`AMP`
`!DFLUX`	Element or element group	Applies distributed heat flux to an element volume or element face.	`AMP`
`!SFLUX`	Surface group	Applies heat flux to a surface group.	`AMP`
`!FILM`	Element or element group	Applies a convection boundary to an element face.	`AMP1`, `AMP2`
`!SFILM`	Surface group	Applies a convection boundary to a surface group.	`AMP1`, `AMP2`
`!RADIATE`	Element or element group	Applies a radiation boundary to an element face.	`AMP1`, `AMP2`
`!SRADIATE`	Surface group	Applies a radiation boundary to a surface group.	`AMP1`, `AMP2`

For !DFLUX, BF represents volumetric heat generation, while S0 through S6 represent heat flux on element faces. For !FILM, element faces are specified by F0 through F6; for !RADIATE, by R0 through R6. Because the correspondence between face numbers and actual element faces depends on the element type, see the reference for each keyword for details.

A convection boundary specifies a convection coefficient and external temperature. A radiation boundary specifies an emissivity-equivalent coefficient and ambient temperature. AMP1 corresponds to the coefficient side, and AMP2 to the external or ambient temperature side, allowing independent time variation for each.

Amplitude Functions¶

An amplitude function defines time variation of a boundary condition or load using a table of times and values. In the input, a named time table is defined with !AMPLITUDE and referenced by the AMP, AMP1, or AMP2 parameter of the target keyword.

The main applicable keywords are as follows.

Structural analysis: !BOUNDARY, !CLOAD, !DLOAD, !SPRING
Dynamic analysis: !VELOCITY, !ACCELERATION
Heat conduction analysis: !FIXTEMP, !CFLUX, !DFLUX, !SFLUX, !FILM, !SFILM, !RADIATE, !SRADIATE

!AMPLITUDE is read in tabular form (DEFINITION=TABULAR). Values are linearly interpolated between tabulated times; before the first tabulated time the first value is used, and after the last tabulated time the last value is used.

The time used to evaluate an amplitude follows the TIME setting in structural static analysis. With STEP TIME (default), it is evaluated using time from the start of the step; with TOTAL TIME, it is evaluated using time from the start of the analysis. In dynamic analysis, it is evaluated using time from the start of the analysis regardless of the TIME setting.

The value type is specified with VALUE. With RELATIVE (default), the amplitude value is multiplied by the value specified for the referencing keyword. With ABSOLUTE in structural analysis, the amplitude value itself is used as the load or boundary-condition value. However, for !BOUNDARY and !SPRING in structural static analysis, the amplitude value is treated as a factor multiplying the value specified for the keyword even when ABSOLUTE is specified.

When !CLOAD and !DLOAD remain active over multiple steps in structural static analysis, if AMP is not specified, from the second step onward the value specified for the keyword is applied directly without multiplying it by the step load factor. When AMP is specified, the amplitude value is followed in every step.

!TEMPERATURE is not subject to amplitude functions.