# Explicit Dynamic Analysis (Radioss Integration)

Explicit Dynamic Analysis in OptiStruct is provided through an integration of the Radioss Starter and Radioss Engine via a translator. Explicit integration schemes, are available via Radioss Integration.

Transparent to you, OptiStruct input data is directly translated into Radioss input data. The Radioss Starter and Radioss Engine are then executed, and the results are brought back into the OptiStruct output module to export the different output formats.

## Solution Method

The basic concepts of the solution methods to highlight the characteristics of the solution methods and to identify the use of certain parameters to control convergence. The solution utilizes a general Newmark integration scheme.

- $$M$$
- Mass matrix
- $$C$$
- Damping matrix
- $$K$$
- Stiffness matrix
- $$f$$
- The vector describes the external loads
- $$u$$
- Displacement vector

The matrix $A$ is the dynamic stiffness. In nonlinear time-dependent problems, this system becomes nonlinear and its solution requires an additional iteration loop at each time step using a Newton-type method.

With ${l}_{c}$ being the critical length of an element and $$c$$ is the speed of sound in the given material.

The element time step based on the critical length of each element is also available. The choice can be made on the XSTEP Bulk Data Entry.

## Problem Setup

Explicit Dynamic Analysis is defined through a SUBCASE.

An XSTEP statement as well as
ANALYSIS=`EXPDYN` must be present in the
subcase. To define the termination time a TTERM Subcase
Information Entry is mandatory. XSTEP references an
XSTEP Bulk Data Entry. Time step control can be defined on
the XSTEP Bulk Data Entry.

The definition of a unit system through the DTI, UNITS or UNITS Bulk Data Entry statement is required.

The Explicit Dynamic Analysis loads and boundary conditions are defined in the Bulk Data Entry section of the input deck. They need to be referenced under the SUBCASE using an SPC, NLOAD, LOAD, IC and RWALL statements in a SUBCASE. Each SUBCASE defines one loading condition that is executed separately.

Subcase continuation is available through the use of CNTNLSUB. Any number of explicit and implicit analyses can be linked. However, explicit (ANALYSIS=EXPDYN) analysis subcases cannot yet be linked with small displacement quasi-static nonlinear (ANALYSIS=NLSTAT) analysis subcases and vice versa.

### Example: Explicit Analysis

```
SUBCASE 3
ANALYSIS = EXPDYN
SPC = 1
NLOAD = 2
XSTEP = 3
TTERM = 1.0
DISP = ALL
STRESS = ALL
BEGIN BULK
XSTEP,3
NLOAD1,2,2,,L,88
TABLED1,88,
+,0.0,0.0,1.0,1.0,ENDT
DTI,UNITS,1,kg,N,m,s
```

### Example: Subcase Continuation

```
DISP = ALL
STRESS = ALL
SUBCASE 1
ANALYSIS = EXPDYN
IC = 5
XSTEP = 4
TTERM = 1.0
SUBCASE 2
ANALYSIS = EXPDYN
IC = 5
XSTEP = 4
TTERM = 1.1
CNTNLSUB = 1
```

## User's Considerations

### Explicit Dynamic Analysis Properties and Materials

Special element types and nonlinear materials are available for Explicit Dynamic Analysis. As a
general rule, property and material definitions that are only applicable in Explicit
Dynamic Analysis are defined on extensions to the original property and to a
MAT1 material, respectively. The extensions are grouped with
the base entry by sharing the same `PID` or `MID`.
In the case of a subcase that is not an Explicit Dynamic Analysis, these extensions
are ignored. Property defaults can be set for shells (XSHLPRM)
and solids (XSOLPRM) that may replace the use of property
extensions.

```
PSHELL, 3, 7, 1.0, 7, , 7
PSHELLX, 3, 24, , , 5
```

```
MAT1, 102, 60.4, , 0.33, 2.70e-6
MATX02, 102, 0.09026, 0.22313, 0.3746, 100.0, 0.175
```

### Coordinate Systems

In Explicit Dynamic Analysis there are moving and fixed coordinate systems. Rectangular coordinate systems that are defined through grid points (CORD1R, CORD3R) are moving with the deformations of the model. Systems defined in terms of point coordinates (CORD2R, CORD4R) are fixed.

The behavior of loads depends on the coordinate system referenced. If the loads
FORCE and MOMENT are desired to be
follower forces, a `CID` that references a moving coordinate system
(CORD1R, CORD3R) must be defined.
Otherwise these loads are not following the deformation. PLOAD
always follows the deformations.

### Characteristics

- In general, a diagonal mass matrix is used
- No matrix factorization necessary
- Equilibrium is always guaranteed
- Maximum stable time step needs to be respected
- Small time steps
- Short-term events

### Limitations

- The following Bulk Data properties and elements are currently not
translated:
- PBUSHT (partially,
`KN`is translated) - PDAMP, CDAMPi
- PGAP, CGAP, CGAPG (partially, friction is not allowed)
- PMASS, CMASSi
- PSHEAR, CSHEAR
- PVISC, CVISC

- PBUSHT (partially,
- Additional relevant Bulk Data Entries (except loads) that are currently not
translated:
- CORD1C, CORD1S, CORD2S
- DMIG
- MAT2, MAT4, MAT5, MAT8, MAT9, MAT10
- MATTi, TABLEST
- MPC, MPCADD
- RBE1, RROD

- Relevant loads that are currently not translated:
- PLOAD1, PLOAD2
- PLOAD4 (partially,
`N1`,`N2`,`N3`cannot be used) - RFORCE (partially,
`RACC`is not supported) - TLOAD1, TLOAD2