Expert systems and finite element structural analysis - a review

Finite element analysis of many engineering systems is practised more as an art than as a science . It involves high level expertise (analytical as well as heuristic) regarding problem modelling (e .g. problem specification,13; choosing the appropriate type of elements etc .), optical mesh design for achieving the specified accuracy (e .g . initial mesh selection, adaptive mesh refinement), selection of the appropriate type of analysis and solution13; routines and, finally, diagnosis of the finite element solutions . Very often such expertise is highly dispersed and is not available at a single place with a single expert. The design of an expert system, such that the necessary expertise is available to a novice to perform the same job even in the absence of trained experts, becomes an attractive proposition. 13; In this paper, the areas of finite element structural analysis which require experience and decision-making capabilities are explored . A simple expert system, with a feasible knowledge base for problem modelling, optimal mesh design, type of analysis and solution routines, and diagnosis, is outlined. Several efforts in these directions, reported in the open literature, are also reviewed in this paper

Consistency aspects of out-of-plane bending, torsion and shear in a quadratic curved beam element

Curved beams in civil engineering applications call for out-of-plane bending and torsion under the action of13; out-of-plane transverse shear loads. The design of a quadratic displacement curved beam element capable of13; representing shear deformation as in the Timoshenko beam theory requires special attention to the manner in which the shear strain is represented. Field-inconsistent representations of the out-of-plane transverse shear strain will result in a loss of efficiency and introduce spurious oscillations in the bending moment, torsional moment and shear force. The optimal field-consistent assumed strain interpolation for shear is derived and it is demonstrated to posses very high accuracy which is free from spurious force and moment oscillations

FEM analysis of LTA-7 horizontal tail

A finite element structural analysis of the stabilizer portion of the horizontal tail has been performed using the MSC/NASTRAN package. The critical loading case is identified by subjecting the structure to loading corresponding to several different load cases. From NASTRAN stress output for these cases, the Va maneuvering 5700 kg ., n = 1.0, 0.2412c, elevator up deflection is seen to be critical. Stresses from this case are used to compute the margins in buckling for skin panels and shear webs. It is seen that stresses are within allowable limits but from the buckling point of view, while the skin panels are over-designed, the midspar web is under-designed and must be stiffened. Comparisons with the stress analysis results from the simple bending theory/shear flow analysis carried out by the ASDE/CAU design group show that there is scope for improvement in the design

Consistency force resultant distributions in displacement elements with varying sectional properties

Force fields computed directly from strains calculated in a displacement type finite element description of a structural element of varying sectional rigidities show extraneous oscillations. The origin of these oscillations is traced to the fact that the displacement type finite element procedure determines strains derived from the displacement field in a least squares correct sense and that force resultants computed using these strain fields and the actual sectional rigidities result in unwanted oscillations. It is necessary to introduce the concept of redistributed assumed force resultant fields that maintain a 'consistent' relationship13; to the strain fields and also are orthogonal to these strain functions. In this paper, the Hu-Washizu theorem is invoked to justify the introduction of an orthogonally correct reconstituted assumed force resultant field which will then be free of extraneous oscillations. The quadratic isoparametric tapered bar element serves to illustrate the underlying principles.13; It follows that the extremely general Hu-Washizu principle is the most practical procedure of implementing an assumed force resultant, assumed strain displacement type formulation to introduce consistency and thereby remove problems associated with field-inconsistency (such as cause locking in constrained media elasticity) and force resultant oscillations due to varying sectional properties

Stress oscillations and spurious load mechanisms in variationally inconsistent assumed strain formulations

Assumed field-consistent strain formulations of the displacement finite element procedure can lead to poor13; convergence and spurious stress oscillations if the assumed strain fields are not variationally correct, ie. they do not satisfy an important orthogonality condition emerging from the equivalence sought between assumed strain displacement procedures and mixed procedures based on the Hellinger-Reissner theorem. Failure to ensure variational correctness introduces errors which can be equated to the presence of spurious loading mechanisms that cause stress oscillations. In this paper, we use the Timoshenko beam element to demonstrate that field-consistency and variational consistency are two complementary but mutually exclusive principlesx2014;one does not imply the other and that both are necessary to successfully implement a displacement type finite element for constrained media

Iterative solver routines (in fortran amp; C) for finite13; element applications

The iterative solution schemes are found to be most effective, in particular when they are used in conjunction with the adaptive mesh refinement concept, for the finite element analysis of large problems.13; Several schemes are developed, implemented (in FORTRAN and C) and tested for their efficiency. The program is made highly user friendly and a typical listing of results is presented in the appendix-B

FEM design and analysis of HAL - Autoclave

Finite Element Structural Analysis of HAL Autoclave System and Components was carried out for the original design under all possible critical load combinations. It was noted that the original design was unsafe from both deformation and stress points of view. Certain design modifications were suggested. Each modification was critically evaluated using simple 1- and 2-dimensional finite element analysis. These modifications were incorporated in the autoclave design and a full-scale finite element analysis was carried out for the modified autoclave system. It was found that the modified system is SAFE from both deformation and stress points of view. MSC-XL is used for finite element modeling and for post-processing the results. MSC/NASTRAN is used for the finite element analysis. FEPACS is used for verification of the MSC/NASTRAN results where necessary

Consistent thermal stress evaluation in finite elements

The computation of thermal stresses in displacement finite elements through a formal theoretical basis using the minimum potential principle leads to oscillating stress predictions. Many finite element packages have therefore used an average temperature in simple elements; thermal stresses were computed only at the centroids of such elements to avoid these problems. In this paper we trace this difficulty to a consistency requirement - requirement that stress fields derived from temperature fields (or initial strains) must be consistent with the total strain field interpolations used in the finite element formulation. The principle governing the problem is developed from the minimum total potential theorem and the Hu-Washizu theorem. This gives it a formal rational basis and leads to an orthogonally condition that provides the procedure for determining consistent, thermal stresses in a variationally correct manner. The principle is demonstrated using some simple problems. A four-noded laminated plane-shell element is also considered to prove the rigour and generality of the approach presented here

Analysis of locking and stress oscillations in a general curved beam element

The exactly integrated general quadratic curved beam element has both membrane and shear locking and significant quadratic oscillations in the axial force and cubic oscillations in the shear force. The functional re-constitution technique is applied to derive accurate error estimates for the manner in which locking is relieved and for the magnitude of the stress oscillations. The orthogonally correct field-consistent interpolations are determined for the optimal form of the element and it is shown that the popular two-point Gaussian integrated13; version of the element is non-orthogonal and has a cubic13; oscillation in the shear force that curiously vanishes at the Barlow points

Field-consistency analysis of 27-noded hexahedral elements for constrained media elasticity

Most 3-dimensional stress analysis is currently performed using the 8-noded linear and the 20-noded quadratic (serendipity) hexahedral elements. Recent experience with the quadratic plate/shell elements show that the 9-noded Lagrangian elements are superior to the 8-noded serendipity elements in applications to thin plate/shell flexure. Extension of this logic suggests that a 27-noded Lagrangian hexahedral element formulation with field-consistency corrections is needed for robust and reliable 3-D modelling of constrained media problems. In this paper we examine the field-consistency aspects involved in the formulation of such an element