A scaled boundary finite element based node-to-node scheme for contact problems.

The analysis of contact problems is a major concern in many engineering applications. It is one of the most difficult topics due to unknown contact areas and inequality constraints. For numerical simulations, the dissimilar discretization of contact interfaces is inevitable due to the tangential slippage in large sliding contact problems. Therefore, it is impossible to maintain the node-to-node (NTN) contact. Various treatments have been proposed to enforce the contact constraints on nonmatching contact interfaces. Their implementations, however, either fail the patch test or require sophisticated algorithms and techniques. This thesis presents a novel NTN contact scheme based on the scaled boundary finite element method (SBFEM). Nonmatching meshes can be converted to matching ones through polytope elements constructed in a SBFEM manner, allowing the use of the simplicity and robustness of a purely nodal based contact formulation. For an individual scaled boundary finite element, the number of edges and faces is not limited and new nodes can be inserted on the element boundary arbitrarily. Only its boundary is discretized and it can be easily extended to include higher order approximations. The contact constraints are enforced by means of complementarity formulations, which are solved as a mixed complementarity problem. This mathematical description not only satisfies the non-penetration condition exactly, but also allows an accurate representation of the second-order Coulomb's friction cone in three dimensions without linearization. Outer iterations of the active contact set are not required. The proposed method is also applied to large sliding contact problems with a mesh updating scheme. The inserted nodes are regarded as auxiliary nodes for the current step. They are removed in a future step to avoid overly-refined mesh. The state variables of newly inserted nodes are updated through interpolation of neighboring nodes. The proposed method is verified by contact problems with analytical solutions, such as the patch test and Mindlin-Hertz contact problem. Significant improvements in higher order elements are obtained by the method when compared with the finite element code ABAQUS. Applications of the method are extended to practical contact problems, where complex geometries are modeled through quadtree or octree meshe

On the equivalence between the cell-based smoothed finite element method and the virtual element method

We revisit the cell-based smoothed finite element method (SFEM) for quadrilateral elements and extend it to arbitrary polygons and polyhedrons in 2D and 3D, respectively. We highlight the similarity between the SFEM and the virtual element method (VEM). Based on the VEM, we propose a new stabilization approach to the SFEM when applied to arbitrary polygons and polyhedrons. The accuracy and the convergence properties of the SFEM are studied with a few benchmark problems in 2D and 3D linear elasticity. Later, the SFEM is combined with the scaled boundary finite element method to problems involving singularity within the framework of the linear elastic fracture mechanics in 2D

A new locking-free polygonal plate element for thin and thick plates based on Reissner-Mindlin plate theory and assumed shear strain fields

A new $n-$ noded polygonal plate element is proposed for the analysis of plate structures comprising of thin and thick members. The formulation is based on the discrete Kirchhoff Mindlin theory. On each side of the polygonal element, discrete shear constraints are considered to relate the kinematical and the independent shear strains. The proposed element: (a) has proper rank; (b) passes patch test for both thin and thick plates; (c) is free from shear locking and (d) yields optimal convergence rates in $L^2-$norm and $H^1-$semi-norm. The accuracy and the convergence properties are demonstrated with a few benchmark examples

The mechanics of delamination in fiber-reinforced composite materials. Part 2: Delamination behavior and fracture mechanics parameters

Based on theories of laminate anisotropic elasticity and interlaminar fracture, the complete solution structure associated with a composite delamination is determined. Fracture mechanics parameters characterizing the interlaminar crack behavior are defined from asymptotic stress solutions for delaminations with different crack-tip deformation configurations. A numerical method employing singular finite elements is developed to study delaminations in fiber composites with any arbitrary combinations of lamination, material, geometric, and crack variables. The special finite elements include the exact delamination stress singularity in its formulation. The method is shown to be computationally accurate and efficient, and operationally simple. To illustrate the basic nature of composite delamination, solutions are shown for edge-delaminated (0/-0/-0/0) and (+ or - 0/+ or - 0/90/90 deg) graphite-epoxy systems under uniform axial extenstion. Three-dimensional crack-tip stress intensity factors, associated energy release rates, and delamination crack-closure are determined for each individual case. The basic mechanics and mechanisms of composite delamination are studied, and fundamental characteristics unique to recently proposed tests for interlaminar fracture toughness of fiber composite laminates are examined

Finite Element Simulation of Dynamic Wetting Flows as an\ud Interface Formation Process

A mathematically challenging model of dynamic wetting as a process of interface formation has been, for the first time, fully incorporated into a numerical code based on the finite element method and applied, as a test case, to the problem of capillary rise. The motivation for this work comes from the fact that, as discovered experimentally more than a decade ago, the key variable in dynamic wetting flows — the dynamic contact angle — depends not just on the velocity of the three-phase contact line but on the entire flow field/geometry. Hence, to describe this effect, it becomes necessary to use the mathematical model that has this dependence as its integral part. A new physical effect, termed the ‘hydrodynamic resist to dynamic wetting’, is discovered where the influence of the capillary’s radius on the dynamic contact angle, and hence on the global flow, is computed. The capabilities of the numerical framework are then demonstrated by comparing the results to experiments on the unsteady capillary rise, where excellent agreement is obtained. Practical recommendations on the spatial resolution required by the numerical scheme for a given set of non-dimensional similarity parameters are provided, and a comparison to asymptotic results available in limiting cases confirms that the code is converging to the correct solution. The appendix gives a userfriendly step-by-step guide specifying the entire implementation and allowing the reader to easily reproduce all presented results, including the benchmark calculations

A Review of Prosthetic Interface Stress Investigations

Over the last decade, numerous experimental and numerical analyses have been conducted to investigate the stress distribution between the residual limb and prosthetic socket of persons with lower limb amputation. The objectives of these analyses have been to improve our understanding of the residual limb/prosthetic socket system, to evaluate the influence of prosthetic design parameters and alignment variations on the interface stress distribution, and to evaluate prosthetic fit. The purpose of this paper is to summarize these experimental investigations and identify associated limitations. In addition, this paper presents an overview of various computer models used to investigate the residual limb interface, and discusses the differences and potential ramifications of the various modeling formulations. Finally, the potential and future applications of these experimental and numerical analyses in prosthetic design are presented

A Comparison of Numerical Methods used for\ud Finite Element Modelling of Soft Tissue\ud Deformation

Soft tissue deformation is often modelled using incompressible nonlinear elasticity, with solutions computed using the finite element method. There are a range of options available when using the finite element method, in particular, the polynomial degree of the basis functions used for interpolating position and pressure, and the type of element making up the mesh. We investigate the effect of these choices on the accuracy of the computed solution, using a selection of model problems motivated by typical deformations seen in soft tissue modelling. We set up model problems with discontinuous material properties (as is the case for the breast), steeply changing gradients in the body force (as found in contracting cardiac tissue), and discontinuous first derivatives in the solution at the boundary, caused by a discontinuous applied force (as in the breast during mammography). We find that the choice of pressure basis functions are vital in the presence of a material interface, higher-order schemes do not perform as well as may be expected when there are sharp gradients, and in general that it is important to take the expected regularity of the solution into account when choosing a numerical scheme

A node-to-node scheme for three-dimensional contact problems using the scaled boundary finite element method

A node-to-node (NTN) scheme for modeling three-dimensional contact problems within a scaled boundary finite element method (SBFEM) framework is proposed. Polyhedral elements with an arbitrary number of faces and nodes are constructed using the SBFEM. Only the boundary of the polyhedral element is discretized to accommodate a higher degree of flexibility in mesh transitioning. Nonmatching meshes can be simply converted into matching ones by appropriate node insertions, thereby allowing the use of a favorable NTN contact scheme. The general three-dimensional frictional contact is explicitly formulated as a mixed complementarity problem (MCP). The inherent nonlinearity in the three-dimensional friction condition is treated accurately without requiring piecewise linearization. Contact constraints for non-penetration and stick-slide are enforced directly in a complementarity format. Numerical examples with 1st and 2nd order elements demonstrate the accuracy and robustness of the proposed scheme

A 2-dimentional contact analysis using second-order virtual element method

In the present study, we exploit the use of second-order virtual element method (VEM) for contact analysis in 2-dimension within the context of linear elasticity and small deformation. By virtue of mesh flexibility in the VEM, the non-matching meshes at the contact interface are transformed into matching meshes, and therefore the node-to-node contact discretization can be constructed. The frictional contact is considered as stick condition, and no tangential movement is allowed due to the assumption of small deformation condition. The normal and frictional contact constraints are imposed using the Lagrange multiplier method and the penalty method, respectively, and the candidate contact interface is determined by a series of adaptive trial and error tests as well as prior experience. Several numerical examples are investigated to illustrate the effectiveness of the proposed method in contact analysis, and the results show that the proposed method is able to handle problem with complex non-matching meshes at contact interface. Properties of shear wall consisting of units with fitting joints are also investigated as a practical application