This paper discusses an approach to controlling two-dimensional local sizing in a bicameral mesh. This concept was introduced in our prior International Meshing Roundtable conference paper, and we expand on it herein. We define bicameral gradation as a mesh size variation of two distinctly different types in two or more separate chambers or subdomains. The first chamber is controlled by constant to local size functions. The second subdomain is governed by a nonlinear sizing function leading to transitioning meshes. A controlled advancing front approach is proposed for both triangular and quadrangular meshes with the singular goal of ensuring a high local quality metric in the first chamber. A modified H-shock sizing scheme governs the second chamber. Virtual mesh topology is constructed at the face boundary both at geometry and node-loop levels to facilitate this type of bicameral meshing. Results clearly indicate the efficacy of the proposed approach leading to both a well-controlled desired size field and high local element quality.

As a feature sensitive meshing investigation, this paper focuses on the identification and meshing of four categories of features specific to automotive body panels, namely beads, fillets, flanges and tabs. An improvised and enhanced medial axis based strategy is proposed for identifying the aforementioned features. Appropriate boundary discretisation, inclusion of zero medial vertex case for annulus identification, medial axis topology modifications to eliminate undesirable pathologies, T-junction squaring with cubic filtering smoothing highlight some of the improvisations to the medial axis technology employed. Ridge curves representing the crest lines of beads and fillets are extracted and inserted on the face. A combination of multi-blocking, clamping and face node-loop insertion, followed by boundary connection strategies are used to generate high fidelity, feature sensitive, quasi-structured meshes.

This paper discusses a new approach to controlling 2D local sizing in a bicameral anisotropic mesh. We define bicameral anisotropy as a mesh size variation of two distinctly different types in two separate chambers or subdomains. The first chamber is controlled by constant to linear local size functions. The second subdomain is governed by a nonlinear sizing function leading to transitioning meshes. A controlled advancing front approach is proposed for both triangular and quadrangular meshes with the singular goal of ensuring a high local quality metric in the first chamber. An H-shock sizing scheme governs the second chamber. Virtual mesh topology is constructed at the face boundary both at geometry and nodeloop levels to facilitate this type of bicameral meshing. Results clearly indicate the efficacy of the proposed approach leading to both a well controlled desired size field and high local element quality.

As a feature sensitive meshing investigation, this paper focuses on beads which are tangent continuous, high curvature, raised surfaces meant to stiffen and enhance the durability and specific strength of automotive body panels. An improvised and enhanced medial axis based strategy is proposed for identifying three broad types of bead features. Appropriate boundary discretisation, inclusion of zero medial vertex case for annulus identification, medial axis topology modifications to eliminate undesirable pathologies, T-junction squaring with cubic filtering smoothing highlight some of the improvisations to the medial axis technology employed. Ridge curves representing the crest lines of the bead are extracted and inserted on the face. A combination of multi-blocking, clamping and face node-loop insertion, followed by boundary connection strategies are used to generate high fidelity, feature sensitive, quasi-structured meshes.

Singularities in structured meshes are vertices that have an irregular valency.The integer irregularity in valency is called the singularity index of the vertex of the mesh. Singularities in cross-fields are closely related which are isolated points where the cross-field vectors are defined in its limit neighbourhood but not at the point itself. For a closed surface the genus determines the minimum number of singularities that are required in a structured mesh or in a cross-field on the surface. Adding boundaries and forcing conformity of the mesh or alignment of the cross-field to them also affects the minimum number of singularities required. In this paper a simple formula is derived from Bunin’s Continuum Theory for Unstructured Mesh Generation (Bunin, 2008) that specifies the net sum of singularity indices that must occur in a cross-field with even numbers of vectors on a face or surface region with alignment conditions. The formula also applies to mesh singularities in quadrilateral and triangle meshes and the correspondence to 3-D hexahedral meshes is related. Some potential applications are discussed.

Cylindrical surfaces of many irregularities populate aerospace and automotive engine components. Many of these surfaces represent power transmitting shafts and rotary mating parts that require structured meshes to expedite contact and other finite element analyses with their mates. This poses a challenge to surface and volume mesh generators. In this paper a novel method of multiblocking based on 2D Cartesian slabs is proposed for the generation of predominantly structured meshes on irregular cylindrical surfaces. A seam generation technique comprises the first step, leading to the creation of an axial line of optimal length to split the 3D surface to facilitate 2D flattened or parametric space generation. The 2D parametric domain of the surface is next transformed to an axis-parallel local coordinate system for Cartesian slab generation. An intricate virtual face split operator is used to dissect the 2d parameter space into parallel rectangular slabs of uniform or varying thicknesses. A light-weight, mesher-native topology builder that uses virtual topological elements is proposed for constructing a virtual topology network of the slabs. Results demonstrate high quality, high fidelity transfinite-dominant meshes on a host of trimmed cylindrical surfaces.

This paper presents a method for creating seams on pipe faces which are effective for reducing the distortion of the face flattening and thus promote the generation of high quality meshes on the faces. The method is applicable to groups of connected B-rep triangulated faces whose underlying surfaces resemble Generalised Cylinders. Isoparametric curves of Generalised Cylinder parametrisations are approximated by establishing singularity-free cross-fields starting with estimated principal curvature directions from which the seams are derived.

A formula is presented for determining the net sum of mesh singularity indices that must occur in an all-quadrilateral (quad) mesh of a face or surface region after the mesh properties have been assigned on the face’s boundaries and according to the face’s Euler Characteristic. The formula is derived from Bunin’s Continuum Theory for Unstructured Mesh Generation [1].

A formula is presented for determining the net sum of mesh singularity indices that must occur in an all-quadrilateral (quad) mesh of a face or surface region after the mesh properties have been assigned on the face’s boundaries and according to the face’s Euler Characteristic. The formula is derived from Bunin’s Continuum Theory for Unstructured Mesh Generation [1]. c © 2017 The Authors. Published by Elsevier Ltd. Peer-review under responsibility of the scientific committee of the 26th International Meshing Roundtable.

Finite element analyses of 3D quadrilateral meshes for automotive body-in-white panels have stringent mesh quality requirements. Several mesh quality metrics, namely element included angles, minimum Jacobian determinant, skew, taper, warp, aspect ratio, minimum element length etc. need to be within acceptable limits. No constitutive relations exist that can tie all these parameters to a single metric that mesh post-processing can target. In the paper presented, a 3D optimization smoothing algorithm is proposed based on element included angles with the constraints of a minimum edge length and geometry fidelity envelope. A complex cost-function is set up for each element based on included element angle at the element corners. Element angle perturbation methods are devised to exercise local control on included angles of quadrilateral and mixed meshes. A minimization principle is worked out to reduce the cost function to an acceptable limit. Goal proximity is defined by acceptable error norms and ranges. Mesh nodes are repositioned iteratively but bound by a geometry fidelity envelope apart from the minimum element edge length constraint. Striking improvement in mesh quality statistics is reported with reasonably monotonic solution convergence patterns.

In this paper, a novel approach to automatically sub-divide a complex geometry and apply an efficient mesh is presented. Following the identification and removal of thin-sheet regions from an arbitrary solid using the thick/thin decomposition approach developed by Robinson et al. [1], the technique here employs shape metrics generated using local sizing measures to identify long-slender regions within the thick body. A series of algorithms automatically partition the thick region into a non-manifold assembly of long-slender and complex sub-regions. A structured anisotropic mesh is applied to the thin-sheet and long-slender bodies, and the remaining complex bodies are filled with unstructured isotropic tetrahedra. The resulting semi-structured mesh possesses significantly fewer degrees of freedom than the equivalent unstructured mesh, demonstrating the effectiveness of the approach. The accuracy of the efficient meshes generated for a complex geometry is verified via a study that compares the results of a modal analysis with the results of an equivalent analysis on a dense tetrahedral mesh.

The creation of idealised, dimensionally reduced meshes for preliminary design and optimisation remains a time-consuming, manual task. A dimensionally reduced model is ideal for assessing design changes through modification of element properties without the need to create a new geometry or mesh. In this paper, a novel approach for automating the creation of mixed dimensional meshes is presented. The input to the process is a solid model which has been decomposed into a non-manifold assembly of smaller volumes with different meshing significance. Associativity between the original solid model and the dimensionally reduced equivalent is maintained. The approach is validated by means of a free-free modal analysis on an output mesh of a gas turbine engine component of industrial complexity. Extensions and enhancements to this work are also discussed.

The finite element method plays an extremely important role in forging process design as it provides a valid means to quantify forging errors and thereby govern die shape modification to improve the dimensional accuracy of the component. However, this dependency on process simulation could raise significant problems and present a major drawback if the finite element simulation results were inaccurate. This paper presents a novel approach to assess the dimensional accuracy and shape quality of aeroengine blades formed from finite element hot-forging simulation. The proposed virtual inspection system uses conventional algorithms adopted by modern coordinate measurement processes as well as the latest free-form surface evaluation techniques to provide a robust framework for virtual forging error assessment. Established techniques for the physical registration of real components have been adapted to localise virtual models in relation to a nominal design model. Blades are then automatically analysed using a series of intelligent routines to generate measurement data and compute dimensional errors. The results of a comparison study indicate that the virtual inspection results and actual coordinate measurement data are highly comparable and the procedures for registration and virtual inspection are computationally efficient, validating the approach as an effective and accurate means to quantify forging error in a virtual environment. Consequently, this provides adequate justification for the implementation of the virtual inspection system in the virtual process design, modelling and validation of forged aeroengine blades in industry.

This paper presents research for developing a virtual inspection system that evaluates the dimensional tolerance of forged aerofoil blades formed using the finite element (FE) method. Conventional algorithms adopted by modern coordinate measurement processes have been incorporated with the latest free-form surface evaluation techniques to provide a robust framework for the dimensional inspection of FE aerofoil models. The accuracy of the approach had been verified with a strong correlation obtained between the virtual inspection data and coordinate measurement data from corresponding aerofoil components.

This paper reports on recent work in the development of a virtual 3D die shape optimisation system for net-shape forging of aerofoil blades for aeroengine applications. Novel computational methods were developed to quantify forging errors during the whole forging cycle including forging, die removal, trimming of flash and cooling. Based on a direct die shape modification method for improved forging precision, a two-weighting factor compensation approach was proposed which proved effective in achieving enhanced dimensional and shape accuracy of forged aerofoil blade. Another key functionality of the optimisation system is a virtual inspection framework, which enables robust validation of forging optimisation results and easy implementation in industrial production. When applied to a Ni-alloy blade test case, the forging optimisation computations rapidly converged and displayed a strong correlation between the forging simulation results and the actual coordinate measurement data.

In this investigation the pulse-echo technique was validated as a method that could be used to monitor the complete polymerization of acrylic bone cement in a surgical theatre. Currently, orthopaedic surgeons have no objective method to quantify the state of cure of bone cement as it progresses through its polymerization cycle. Clear benefits of the pulse-echo technique are that it is easy to use, non-invasive, and non-destructive. Furthermore, the test results were found to be highly reproducible with minor deviations. Three proprietary cements were used to confirm the validity of the technique; CMW Endurance, Palacos R and Simplex P. The results showed that the acoustic properties of bone cement clearly demonstrated a relationship with the different stages of polymerization, and in particular with the transitions between the waiting, dough, and setting phases. Additionally, the cure time of the poly(methyl methacrylate) cements consistently correlated with the attainment of 75 per cent of the average maximum velocity of sound value. The measured cure times concurred with the ISO and ASTM standards. Moreover, measurements of the final sound velocity and broadband ultrasonic attenuation correlated strongly with the density and mechanical properties of the cured bone cement samples.

Acrylic bone cement is weakened by its porosity, which promotes the formation of microcracks, which contribute to major crack propagation and ultimately failure of the cement mantle. Bone cement mixing techniques play a significant role in determining the quality of bone cement produced. A high degree of porosity is found to exist in cement that is inadequately mixed. Current commercial bone cement mixing systems allow for the preparation of the bone cement under the application of a vacuum in a closed, sealed chamber by means of a repeatable mixing action. These mixing systems are perceived to be repeatable and reliable by orthopaedic community. In this paper, the quality of bone cement mixed using an operator independent bone cement mixing system was compared with that of cement prepared using commercially available devices. The results of the investigation highlighted that cement prepared using the automated, repeatable mixing regime that is operator independent demonstrated consistently better physical and mechanical properties in comparison with cement mixed using proprietary cement mixing devices. Furthermore, Design of Experiments software established the optimal factors that influenced the physical and mechanical properties of PMMA bone cement.