Sunil Saigal

A survey of recent shell finite elements

Since the mid-1960s when the forms of curved shell finite elements were originated, including those pioneered by Professor Gallagher, the published literature on the subject has grown extensively. The first two present authors and Liaw presented a survey of such literature in 1990 in this journal. Professor Gallagher maintained an active interest in this subject during his entire academic career, publishing milestone research works and providing periodic reviews of the literature. In this paper, we endeavor to summarize the important literature on shell finite elements over the past 15 years. It is hoped that this will be a befitting tribute to the pioneering achievements and sustained legacy of our beloved Professor Gallagher in the area of shell finite elements. This survey includes: the degenerated shell approach; stress-resultant-based formulations and Cosserat surface approach; reduced integration with stabilization; incompatible modes approach; enhanced strain formulations; 3-D elasticity elements; drilling d.o.f. elements; co-rotational approach; and higher-order theories for composites. Copyright

H-Morph: An indirect approach to advancing front hex meshing

H-Morph is a new automatic algorithm for the generation of a hexahedral-dominant finite element mesh for arbitrary volumes. The H-Morph method starts with an initial tetrahedral mesh and systematically transforms and combines tetrahedra into hexahedra. It uses an advancing front technique where the initial front consists of a set of prescribed quadrilateral surface facets. Fronts are individually processed by recovering each of the six quadrilateral faces of a hexahedron from the tetrahedral mesh. Recovery techniques similar to those used in boundary constrained Delaunay mesh generation are used. Tetrahedra internal to the six hexahedral faces are then removed and a hexahedron is formed. At any time during the H-Morph procedure a valid mixed hexahedral–tetrahedral mesh is in existence within the volume. The procedure continues until no tetrahedra remain within the volume, or tetrahedra remain which cannot be transformed or combined into valid hexahedral elements. Any remaining tetrahedra are typically towards the interior of the volume, generally a less critical region for analysis. Transition from tetrahedra to hexahedra in the final mesh is accomplished through pyramid-shaped elements. Advantages of the proposed method include its ability to conform to an existing quadrilateral surface mesh, its ability to mesh without the need to decompose or recognize special classes of geometry, and its characteristic well-aligned layers of elements parallel to the boundary. Example test cases are presented on a variety of models. Copyright

Cohesive element modeling of viscoelastic fracture : Application to peel testing of polymers

A computational modeling technique for fracture propagation in viscoelastic materials using cohesive elements for the zone ahead of the crack tip is presented. The computational technique is used to study the problem of increase in fracture energy with peel velocity in peel testing of polymers. A rate-independent phenomenological cohesive zone model is used to model the intrinsic fracture toughness of the interface between the polymer sheets. A dimensional analysis reveals that the macroscopic fracture energy scales with the intrinsic fracture toughness and is a function of peel velocity, and parameters such as the thickness, bulk properties of the polymer sheets, and other cohesive zone properties. The growth of fracture energy as a function of the peel velocity has been studied for polymer sheets characterized by a standard linear viscoelastic solid. Viscoelastic losses in the peel arm vanish in the limits of very slow and rapid peeling. Peak dissipation is obtained at an intermediate velocity, which is related to the characteristic relaxation time and thickness. This behavior is interpreted in terms of the size of elastic and viscous zones near the crack tip. It is found that the total energy dissipated is dependent upon both the intrinsic fracture toughness and the characteristic opening displacement of the cohesive zone model. The computational framework has been used to model experimental data on peeling of Butadiene rubbers. It is found that the usual interpretation of these data, that the macroscopic dissipation equals the rate-independent intrinsic toughness multiplied by a factor that depends on rate of loading, leads to a large quantitative discrepancy between theory and experiment. It is proposed that a model based on a rate-dependent cohesive law be used to model these peel tests.

Geometrically Nonlinear Finite Element Analysis of Imperfect Laminated Shells

Formulations and computational procedures are presented for the finite element analysis of laminated anisotropic composite thin shells including imperfections. The derivations of the nonlinear geometric element stiffness matrices were based on the total Lagrangian description. A 48 degree-of-freedom (d.o.f.) general curved shell element with arbitrary distribution of curvatures was used to model the shell middle- surface. Numerical results include the large deflection behavior of a variety of perfect plate and shell examples; buckling of a spherical shell with an axially symmetric im perfection ; and buckling of a cylindrical panel using measured initial transverse im perfections. A good comparison with existing results is obtained.

Extensible plastic collapse of thin-wall frusta as energy absorbers

Abstract The crumpling of thin-walled frusta, under axial compression, in the ‘concertina’ mode is studied. The energy expended in bending at the plastic hinges and in stretching the metal between the hinges is minimized for the total decrease in height due to collapse. The thinning of the cross-section due to stretching is neglected. A theoretical model has been developed and numerical results are obtained that show the effect of slenderness, t/ D , and the semi-apical angle of the frusta. Good qualitative agreement in trends is exhibited when comparison with available experimental results is made.

Polymer interfacial fracture simulations using cohesive elements

A family of cohesive elements is presented based on cohesive zone models to describe polymer interfacial fracture. Their capabilities are demonstrated in three case studies of interfacial failure. The first is a simulation of the t-peel test for the determination of adhesion between two elastomers. This case is characterized by large, inelastic deformation that is difficult to model using classical fracture mechanics and analytic cohesive zone approaches. The formulation allows simulation of crack growth in the presence of large global strains and the identification of peak viscous loss zones in the peel arms. The second case study is the analysis of a compressive shear test to determine adhesion between a viscoelastic elastomer and a rigid substrate. An experimentally observed transition from stable to unstable fracture is described accurately by the model, providing appropriate cohesive zone parameters are established. The third example treats interfacial failure in a multilayer elasto-plastic polymer system. The approach illustrates a capability to capture crack nucleation and propagation in systems with complex microstructures comprising of multiple layered phases and associated interfaces.

Advances of thin shell finite elements and some applications—version I

Abstract A first attempt is made to review the advances of the formulations for thin shell finite elements in the form of flat plates, axisymmetrical shells and curved shells. The Discrete Kirchhoff Theory shell elements and the degenerated shell elements are discussed. Experiences in shear and membrane lockings are elaborated. The survey is further illustrated with some extensions and applications to cases such as static and dynamic responses, static and dynamic bucklings, laminated composites, random loadings and random structural and material properties. In all cases, studies of the effects of geometric and material nonlinearities are discussed.

An arbitrary condensing, noncondensing solution strategy for large scale, multi-zone boundary element analysis

A multi-zone boundary element analysis (BEA) capability that includes substructuring and condensation in a completely general fashion is presented. This condensation procedure is shown to be an effective way to perform blocked matrix factorizations using a reduced amount of high speed computer memory, and an approach that largely removes the effect of the boundary element zone numbering scheme on the computational resources expended due to block fill-in. In iterative problems with changing configuration, the strategy of condensing (substructuring) the unchanging portion of an overall model, in an exact fashion, and subsequently iterating on the resulting reduced model, is shown to have the potential for extending the range of such iterative problems. The approach will also allow for the simultaneous condensation and subsequent expansion of multiple boundary element zones on computers with parallel processing facility. The overall algorithm is described that allows for the assembly and solution of boundary element zones connected in a quite general way that may also be arbitrarily either condensed or maintained at their original size. The approach thus allows for both condensed and uncondensed boundary element zones to consistently coexist in the same multi-zone problem. A consistent and general formulation for the treatment of the double values of traction components at boundary element zone corners is also presented. Sample problems are described to demonstrate the efficiency and usefulness of the resulting capability.

Boundary element implicit differentiation equations for design sensitivities of axisymmetric structures

Abstract Design sensitivity analysis of axisymmetric elastic media is formulated using boundary elements. The kernels for sensitivity matrices are obtained through implicit differentiation of the corresponding boundary element elasticity kernels. The singular terms are obtained by applying the boundary displacements and tractions, and their respective sensitivities for the rigid body motion mode and the inflation mode. The equations for the recovery of sensitivities of axisymmetric boundary stresses are presented. As a check on accuracy, the approach is applied to a series of examples for which analytical elasticity solutions are available. The predictions for both displacement- and stress-sensitivities are accurate. Additional examples are provided to demonstrate the versatility of the present approach.

A THREE-DIMENSIONAL ELEMENT-FREE GALERKIN ELASTIC AND ELASTOPLASTIC FORMULATION

A small strain, three-dimensional, elastic and elastoplastic Element-Free Galerkin (EFG) formulation is developed. Singular weight functions are utilized in the Moving-Least-Squares (MLS) determination of shape functions and shape function derivatives allowing accurate, direct nodal imposition of essential boundary conditions. A variable domain of influence EFG method is introduced leading to increased efficiency in computing the MLS shape functions and their derivatives. The elastoplastic formulations are based on the consistent tangent operator approach and closely follow the incremental formulations for non-linear analysis using finite elements. Several linear elastic and small strain elastoplastic numerical examples are presented to verify the accuracy of the numerical formulations. Copyright