# ADINA system

*automatic dynamic incremental non-linear analysis system*

The finite-element method (cf. also Difference scheme, variational) is nowadays (1990s) widely used for the analysis of engineering problems, in research, design and manufacturing. The problems solved fall into the areas of solid and structural mechanics, fluid mechanics, and the interaction between fluids and structures. The name ADINA stresses that automatic procedures are used and very general analysis problems can be solved. ADINA has been developed to address many engineering and scientific problems in these areas.

The first step of any analysis is to choose an appropriate mathematical model. Once the mathematical model has been selected, the finite-element method is used to solve this model. This solution entails the mesh generation, imposition of the boundary conditions, establishment and solution of the governing finite-element equations, and the assessment of the numerical error. A finite-element system should be usable for performing these tasks with as little human effort as possible.

Since major design decisions are based on results of finite-element analysis, the reliability and effectiveness of the finite-element solution procedures employed are of utmost importance. A strong mathematical basis for these procedures is therefore required, and much research effort has been expended to develop finite-element methods that are strong in theory and practice.

The solution techniques used in the ADINA system are documented in [a1], [a2], [a3]. Specifically, [a1] gives the theoretical basis of the finite-element procedures used. Many applications are presented in [a4].

## Contents

## Solution of solids and structures.

The finite-element discretization schemes employed for the solution of solids and structures are the standard displacement method and mixed methods. The standard displacement method, while quite effective in general two- and three-dimensional analysis, is not efficient for the analysis of (almost) incompressible response (such as encountered in the analysis of rubber-like materials and elasto-plastic, creep or visco-plastic materials) and for the analysis of plates and shells. The basic difficulty encountered is that of "solution locking" . Mathematically, solution locking means that the convergence rate is highly dependent upon the bulk modulus (in almost incompressible analysis) or the thickness dimension (in the analysis of plates and shells) and decreases drastically, respectively, as the bulk modulus increases and the thickness dimension decreases. For incompressible analysis, the ADINA system offers the use of displacement/pressure-based elements which satisfy the inf-sup condition, and hence are stable and optimal. These elements can be employed for linear and highly non-linear analysis [a1]. For the solution of plate and shell problems the system offers the use of elements based on mixed interpolation, that is, the MITC elements, and special transition elements to model transitions between three-dimensional and shell actions [a1]. Isotropic, orthotropic and general composite plates and shells can be analyzed.

Finite-element discretizations can be used to solve for static or dynamic, linear or non-linear response. The non-linearities can be due to large deformations and/or non-linear constitutive relations. A library of material models is available to model many materials used in engineering practice, and the user can incorporate a private material model as well.

Another important solution procedure available in the ADINA system is the contact algorithm, which is based on the constraint-function method [a1].

## Solution of heat transfer in solids.

In many structural analyses, notably in mechanical engineering, temperature effects must be included in the stress solution. For such analyses the ADINA system offers a thermal analysis capability for general two- and three-dimensional solids and shell structures. Convection and general radiation boundary conditions can be modelled and steady-state or transient conditions can be considered. Also, the constitutive relations can be temperature- or time-dependent.

Of course, these capabilities can also be used to solve other field problems such as seepage and electrostatic conditions [a1].

## Solution of fluid flows including structural interactions.

A large area of analysis application is the solution of fluid flows. Using the ADINA system the fluid can be modelled as an incompressible or compressible fluid governed by the full Navier–Stokes equations [a1], [a2], [a3]. The constitutive relations can be highly non-linear, and various turbulence models can be employed. Hence the full range of flows, from Stokes flows to highly compressible flows with shock fronts, can be analyzed. The discretization schemes used are a combination of finite-element and finite-volume procedures [a1], [a2], [a3].

For compressible flows the Euler equations used to model flows can also be solved (cf. also Euler equation).

A particularly valuable feature is the capability of analyzing fluid flows with structural interactions. In such solutions an arbitrary Lagrangian–Eulerian formulation is used, and the full flow and structural analysis capabilities of the ADINA system can be employed. Hence, for example, the flow can be fully compressible and the structure can include large deformations and non-linear material response.

## Solution of equations.

A key step in the finite-element process is the solution of the equations. The ADINA system offers direct sparse solution schemes as well as iterative solution procedures. In structural analysis one frequently uses the sparse solver, but for very large models the iterative conjugate-gradient procedure with pre-conditioning, available in the ADINA system, is attractive. For fluid flows, of course, one mostly uses iterative procedures, and a bi-conjugate-gradient technique and a GMRES method, with pre-conditioning, are available.

## Parallel processing.

In recent years, parallel processing has become a most important feature of finite-element programs. The ADINA system, except for the pre- and post-processing programs, has been fully parallelized for certain machines. Domain decomposition is performed automatically, and the parallelization embraces the calculation and assemblage of the element matrices, the solution of the equations, and the calculation of the element results.

## Use of the ADINA system.

The ADINA programs are used worldwide in research, industry and education, and increasingly in conjunction with CAD programs. Many diverse applications have been published at the ADINA Conferences [a4].

#### References

[a1] | K.J. Bathe, "Finite element procedures" , Prentice-Hall (1996) |

[a2] | ADINA R&D Inc., "ADINA: Theory and Modeling Guide" , Reports ARD 97–7; 97–8 , ADINA R&D Inc. (1997) |

[a3] | K.J. Bathe, "Simulation of structural and fluid flow response in engineering practice" Computer Modelling and Simulation in Engineering , 1 (1996) pp. 47–77 |

[a4] | "Nonlinear finite element analysis and ADINA. Computers and Structures. 9–11th ADINA Conf. Proc." K.J. Bathe (ed.) , 47 (4/5); 56 (2/3); 64 (5/6) , Pergamon (1993–1997) |

**How to Cite This Entry:**

ADINA system. K.J. Bathe (originator),

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=ADINA_system&oldid=14399