Automated mixed dimensional modelling from 2D and 3D CAD models

The motivation for this paper is to present procedures for automatically creating idealised finite element models from the 3D CAD solid geometry of a component. The procedures produce an accurate and efficient analysis model with little effort on the part of the user. The technique is applicable to thin walled components with local complex features and automatically creates analysis models where 3D elements representing the complex regions in the component are embedded in an efficient shell mesh representing the mid-faces of the thin sheet regions. As the resulting models contain elements of more than one dimension, they are referred to as mixed dimensional models. Although these models are computationally more expensive than some of the idealisation techniques currently employed in industry, they do allow the structural behaviour of the model to be analysed more accurately, which is essential if appropriate design decisions are to be made. Also, using these procedures, analysis models can be created automatically whereas the current idealisation techniques are mostly manual, have long preparation times, and are based on engineering judgement. In the paper the idealisation approach is first applied to 2D models that are used to approximate axisymmetric components for analysis. For these models 2D elements representing the complex regions are embedded in a 1D mesh representing the midline of the cross section of the thin sheet regions. Also discussed is the coupling, which is necessary to link the elements of different dimensionality together. Analysis results from a 3D mixed dimensional model created using the techniques in this paper are compared to those from a stiffened shell model and a 3D solid model to demonstrate the improved accuracy of the new approach. At the end of the paper a quantitative analysis of the reduction in computational cost due to shell meshing thin sheet regions demonstrates that the reduction in degrees of freedom is proportional to the square of the aspect ratio of the region, and for long slender solids, the reduction can be proportional to the aspect ratio of the region if appropriate meshing algorithms are used.

Parametric CAD model based shape optimization using adjoint functions

Adjoint methods have proven to be an efficient way of calculating the gradient of an objective function with respect to a shape parameter for optimisation, with a computational cost nearly independent of the number of the design variables [1]. The approach in this paper links the adjoint surface sensitivities (gradient of objective function with respect to the surface movement) with the parametric design velocities (movement of the surface due to a CAD parameter perturbation) in order to compute the gradient of the objective function with respect to CAD variables.
For a successful implementation of shape optimization strategies in practical industrial cases, the choice of design variables or parameterisation scheme used for the model to be optimized plays a vital role. Where the goal is to base the optimization on a CAD model the choices are to use a NURBS geometry generated from CAD modelling software, where the position of the NURBS control points are the optimisation variables [2] or to use the feature based CAD model with all of the construction history to preserve the design intent [3]. The main advantage of using the feature based model is that the optimized model produced can be directly used for the downstream applications including manufacturing and process planning.
This paper presents an approach for optimization based on the feature based CAD model, which uses CAD parameters defining the features in the model geometry as the design variables. In order to capture the CAD surface movement with respect to the change in design variable, the “Parametric Design Velocity” is calculated, which is defined as the movement of the CAD model boundary in the normal direction due to a change in the parameter value.
The approach presented here for calculating the design velocities represents an advancement in terms of capability and robustness of that described by Robinson et al. [3]. The process can be easily integrated to most industrial optimisation workflows and is immune to the topology and labelling issues highlighted by other CAD based optimisation processes. It considers every continuous (“real value”) parameter type as an optimisation variable, and it can be adapted to work with any CAD modelling software, as long as it has an API which provides access to the values of the parameters which control the model shape and allows the model geometry to be exported. To calculate the movement of the boundary the methodology employs finite differences on the shape of the 3D CAD models before and after the parameter perturbation. The implementation procedure includes calculating the geometrical movement along a normal direction between two discrete representations of the original and perturbed geometry respectively. Parametric design velocities can then be directly linked with adjoint surface sensitivities to extract the gradients to use in a gradient-based optimization algorithm.
The optimisation of a flow optimisation problem is presented, in which the power dissipation of the flow in an automotive air duct is to be reduced by changing the parameters of the CAD geometry created in CATIA V5. The flow sensitivities are computed with the continuous adjoint method for a laminar and turbulent flow [4] and are combined with the parametric design velocities to compute the cost function gradients. A line-search algorithm is then used to update the design variables and proceed further with optimisation process.

FEM Analysis to Optimally Design End Mill cutters for Milling of Ti-6Al-4V

This paper presents an FEM analysis conducted for optimally designing end mill cutters through verifying the cutting tool forces and stresses for milling Titanium alloy Ti-6Al-4 V. Initially, the theoretical tool forces are calculated by considering the cutting edge on a cutting tool as the curve of an intersection over a spherical/flat surface based on the model developed by Lee & Altinas [1]. Considering the lowest tool forces the cutting tool parameters are taken and optimal design of end mill is decided for different sizes. Then the 3D CAD models of the end mills are developed and used for Finite Element Method to verify the cutting forces for milling Ti-6Al-4 V. The cutting tool forces, stress, strain concentration (s), tool wear, and temperature of the cutting tool with the different geometric shapes are simulated considering Ti-6Al-4 V as work piece material. Finally, the simulated and theoretical values are compared and the optimal design of cutting tool for different sizes are validated. The present approach considers to improve the quality of machining surface and tool life with effects of the various parameters concerning the oblique cutting process namely axial, radial and tangential forces. Various simulated test cases are presented to highlight the approach on optimally designing end mill cutters.

Determining the parametric effectiveness of a CAD model

The motivation for this paper is to present an approach for rating the quality of the parameters in a computer-aided design model for use as optimization variables. Parametric Effectiveness is computed as the ratio of change in performance achieved by perturbing the parameters in the optimum way, to the change in performance that would be achieved by allowing the boundary of the model to move without the constraint on shape change enforced by the CAD parameterization. The approach is applied in this paper to optimization based on adjoint shape sensitivity analyses. The derivation of parametric effectiveness is presented for optimization both with and without the constraint of constant volume. In both cases, the movement of the boundary is normalized with respect to a small root mean squared movement of the boundary. The approach can be used to select an initial search direction in parameter space, or to select sets of model parameters which have the greatest ability to improve model performance. The approach is applied to a number of example 2D and 3D FEA and CFD problems.

Aerodynamic optimization using Adjoint methods and parametric CAD models

This paper describes an implementation of a method capable of integrating parametric, feature based, CAD models based on commercial software (CATIA) with the SU2 software framework. To exploit the adjoint based methods for aerodynamic optimisation within the SU2, a formulation to obtain geometric sensitivities directly from the commercial CAD parameterisation is introduced, enabling the calculation of gradients with respect to CAD based design variables. To assess the accuracy and efficiency of the alternative approach, two aerodynamic optimisation problems are investigated: an inviscid, 3D, problem with multiple constraints, and a 2D high-lift aerofoil, viscous problem without any constraints. Initial results show the new parameterisation obtaining reliable optimums, with similar levels of performance of the software native parameterisations. In the final paper, details of computing CAD sensitivities will be provided, including accuracy as well as linking geometric sensitivities to aerodynamic objective functions and constraints; the impact in the robustness of the overall method will be assessed and alternative parameterisations will be included.

Strategies for adding features to CAD models in order to optimize performance

This paper presents an approach which enables new parameters to be added to a CAD model for optimization purposes. It aims to remove a common roadblock to CAD based optimization, where the parameterization of the model does not offer the shape sufficient flexibility for a truly optimized shape to be created. A technique has been developed which uses adjoint based sensitivity maps to predict
the sensitivity of performance to the addition to a model of four different feature types, allowing the feature providing the greatest benefit to be selected. The optimum position to add the feature is also discussed. It is anticipated that the approach could be used to iteratively add features to a model, providing greater flexibility to the shape of the model, and allowing the newly-added parameters to be used as design variables in a subsequent shape optimization.

Modelling 3D camera movement for vibration characterisation and multiple object identification with application to lighting assessment

Utilising cameras as a means to survey the surrounding environment is becoming increasingly popular in a number of different research areas and applications. Central to using camera sensors as input to a vision system, is the need to be able to manipulate and process the information captured in these images. One such application, is the use of cameras to monitor the quality of airport landing lighting at aerodromes where a camera is placed inside an aircraft and used to record images of the lighting pattern during the landing phase of a flight. The images are processed to determine a performance metric. This requires the development of custom software for the localisation and identification of luminaires within the image data. However, because of the necessity to keep airport operations functioning as efficiently as possible, it is difficult to collect enough image data to develop, test and validate any developed software. In this paper, we present a technique to model a virtual landing lighting pattern. A mathematical model is postulated which represents the glide path of the aircraft including random deviations from the expected path. A morphological method has been developed to localise and track the luminaires under different operating conditions. © 2011 IEEE.