### The Preferred Finite Element Program for Linear and Nonlinear Structural Analysis

ADINA is the premier finite element program for state-of-the-art stress analysis of solids and structures in statics and dynamics. The ADINA program offers versatile and generally applicable finite elements for solids, trusses, beams, pipes, plates, shells, and gaps. The analysis can be linear or highly nonlinear, including effects of material nonlinearities, large deformations, temperature dependency, and contact conditions.

The ADINA system was developed from the beginning to solve difficult nonlinear problems in diverse engineering disciplines. Continuous feedback from our customers for over 30 years has strengthened and enhanced the features in ADINA.

### Linear Analysis

ADINA linear analysis applies to problems that meet linear assumptions: materially linear, small displacement formulations, and constant boundary conditions. If any of the above assumptions is not satisfied, the problem should be solved with nonlinear analysis assumptions.

ADINA linear analysis includes linear static analysis and linear dynamic analysis. For linear static analysis, the finite element system of equilibrium equations needs to be solved once, and no time integration is required. For dynamic analysis (linear or nonlinear), the step-by-step direct integration method is the default for the time integration. While for linear dynamic analysis, besides direct integration, the time history mode superposition method can be used in ADINA, which is more effective when the time integration has to be carried out over many time steps, for example, in earthquake analysis.

Steel ball impacting and punching through a thin plate

### Nonlinear Analysis

ADINA can perform the following basic kinds of nonlinear analysis: materially-nonlinear-only, geometrically nonlinear with small strains, and geometrically nonlinear with large strains. These fundamental formulations encompass many different modeling situations. Different regions of the model can use different nonlinear analysis assumptions.

The same elements are available for both linear and nonlinear analysis, thus a linear model can easily be converted into a nonlinear model.

For difficult nonlinear problems, the load increments can be cut back automatically, and for problems involving snap-through or snap-back behavior, a load-displacement-control algorithm can trace the solution response.

### Elements

ADINA includes both continuum elements (2-D and 3-D solid elements), and also structural elements (truss, beam, pipe, shell, spring). These elements are formulated for use in both linear and nonlinear analysis. For example, the shell elements can be effectively used in the analysis of thick and thin shells, under linear, materially nonlinear and geometrically nonlinear conditions. User-coded subroutines may also be implemented and linked to ADINA to include user-defined element definitions.

Automobile mesh consisting of continuum and structural elements

Stretching of a rubber component using the Mooney-Rivlin material model

### Material Models

ADINA offers a rich library of material models for simulations involving a wide variety of engineering materials under diverse conditions. In addition to linearly elastic isotropic and anisotropic material models, ADINA supports numerous viscoelastic and plasticity models appropriate for modeling ductile metals, polymers, and geotechnical materials. Creep effects resulting from thermal effects and neutron-rich environments can also be modeled. Other advanced models include the Potential-based Fluid, Piezoelectric, Gasket, and Three-Network models.

ADINA's supported hyperelastic models are appropriate for modeling elastomers (e.g., rubbers, foams, etc.) and soft biological tissues, for example. All hyperelastic models can include time-dependent viscoelasticity, material anisotropy, and/or Mullins-type damage effects. These behaviors can be important for capturing the response of filled rubbers or materials possessing "preferred" directions due to internally oriented families of reinforcing fibers. Of course, temperature effects (i.e., softening, expansion) can be included via Thermal-Mechanical Coupling (TMC) or Fluid-Structure Interaction (FSI) coupling.

### Contact Mechanics

ADINA provides a variety of advanced contact algorithms for modeling contact mechanics involving solid elements (2-D and 3-D solids) and structural elements (truss, beam, iso-beam or axisymmetric shell, plate, shell and pipe elements). Only very general contact conditions are assumed: the points of contact are assumed not know a priori, both sticking and sliding can be modeled, repeated contact and separation between multiple bodies is permitted, self-contact and double-sided contact are permitted, tied contact can be modeled, friction can be modeled according to various friction laws, and node-to-segment or node-to-node contact can be assumed. These general contact assumptions make ADINA an attractive resource for modeling contact mechanics in a variety of situations.

In finite element models that contain regions of a fine mesh and others of a coarse mesh, or in models that contain areas of free-form tetrahedral meshing and others of mapped, brick meshing, ADINA offers the glue-mesh feature. The glue-mesh feature allows the connection of these regions with dissimilar meshes, and can be applied in two- or three-dimensional cases.

Crushing of an automobile door using self-contact analysis

Impact test of bicycle helmet

### Dynamic Analysis

ADINA is the premier code for implicit dynamic analyses. Implicit time integration schemes must be employed when numerical stability and solution accuracy cannot be compromised. For example, the analyst need not select a time step to ensure stability. Rather, in implicit analyses, the time step can be chosen purely on the basis of the problem's physical characteristics (e.g., to capture a physical response). Aside from supporting the standard Newmark method, ADINA is the only finite element code to support the Bathe time implicit time integration method, which offers superior stability while accurately capturing resolvable modes and automatically suppressing spurious high-frequency responses.

There are situations in which implicit methods are simply too expensive or fail to converge. High speed impact and wave propagation problems (e.g., shocks and explosions) with perhaps millions of time steps are good candidates for explicit methods, which do not require factorization or iterative solution of the system of equations. ADINA is the only code to support the Noh-Bathe explicit method, which also suppresses spurious frequency modes from the solution without the need for specifying unphysical parameters. Of course, ADINA also supports the standard central-difference method.

### Frequency Analysis

The ADINA system includes several capabilities for the characterization of a structural response using frequency domain analysis. The dynamic structural response submitted to a given excitation described by a response spectrum can be investigated. These are ground or support motions typical of earthquakes or shocks. Additionally, a Fourier analysis of the time history of a point in the structure can be performed. Structural responses to harmonic or random vibrations, whether from a base motion or from applied forces, can be analyzed. Finally, the response of a Single Degree of Freedom (SDOF) system connected to the finite element model can also be investigated.

An important capability available in ADINA is that frequencies and mode shapes can be computed in nonlinear analysis. These analyses may contain geometric and material nonlinear conditions including contact, and the frequencies and mode shapes can be obtained at any solution step of the nonlinear analysis. The calculation can be performed using the subspace iteration method or the Lanczos method.

Mode frequency analysis of a car wheel

Collapse of Underwater Pipe

### Buckling and Post-buckling Analysis

Safety assessment in modern structural engineering must include the possibility of the structure failing by local or global buckling. Buckling involves complex interactions between geometrical and material effects, requiring state-of-the-art formulations for an accurate solution.

ADINA is well suited for the calculation of buckling and post-buckling behavior. A special linearized buckling analysis feature is available for the prediction of buckling loads and associated buckling mode shapes. The buckling mode shapes can then be applied to the structure in the form of geometric imperfections, to create an "imperfect" structural model. The imperfect model can then be analyzed to obtain the response at various load levels, in order to determine the load required to collapse the structure. One technique especially well-suited to type of analysis is the load-displacement-control algorithm available in ADINA. This algorithm allows the collapse load, and also the post-buckling response (with snap-through or snap-back behavior) to be calculated with minimal input from the user.

### Other Capabilities

ADINA also provides many additional capabilities for structural analysis.

- Cyclic symmetry analysis is useful for components where the geometry and boundary conditions are rotationally symmetric. It can be applied to static, dynamic and frequency analyses. The memory required for cyclic symmetry analysis is typically an order of magnitude less than that required for the full analysis, and the solution time can also be an order of magnitude smaller.
- Restart analysis is also a useful feature in ADINA. It can be used when the user wishes to continue an analysis beyond its previous end point, or to change the analysis type, loads or boundary conditions or tolerances. It supports restarting from static to dynamic analyses as well as switching between implicit and explicit dynamics.
- In addition, the 3D-iterative solver in ADINA can efficiently solve large models containing mainly higher-order elements in linear and nonlinear analyses, including contact.