3D modelling and the use of numeric simulations in the early phases of the development of products has become in the industry over the past few decades regular practice. In the desire for even greater competitiveness of products, they began, together with numeric analyses to also use optimisation methods. Above all, size optimisation and form optimisation are used, while in recent times also topology optimisation has also begun to become established. This has very much advanced in the last decade together with the development of 3D printing. If we add to this the fact that the modern optimisation of topology is also all the more capable of delivering a form, which are suitable for classic production (for example: casting, forging, welding), it becomes clear that the optimisation of topology has, or sooner or later, will very much return to the early phases of planning the supporting structure of parts.
3D modelling
Fundamental principles of 3D modelling
3D modelling, as a part of computer graphics, is closely connected with mathematics, above all, linear algebra. It has to do with the process of creating a mathematical representation of a three-dimensional object. This process enables the computer to show represented objects on a two-dimensional screen which we call 3D modelling. 3D modelling is founded on mathematics and physics.
Creating mathematical representations of three-dimensional objects, or 3D modelling, can be achieved in two ways: with the use of tools in programs for modelling or directly with programming and the use of mathematical equations. The use of such intended tools is a more simplified approach, as it enables the designer significantly greater control over the shape of the model. Such programs are written in the background by equations which suit the model on the screen, while designers take care of nothing more than the look of the model.
During the use of such programs, the computer shows a visual representation of our objects, while in the background it operates with a large number of data, typically stored in matrixes. The result of this kind of creation we call a 3D model.
3D modelling and topology in practice in engineering
3D modelling and the use of numeric simulations in the early phases of the development of products has in the industry, over the past few decades, become regular practice. In the desire for even greater competitiveness of products, they began, together with numeric analyses to also use optimisation methods. Above all, size optimisation and form optimisation are used, while in recent times also topology optimisation has also begun to become established. This has very much advanced in the last decade together with the development of 3D printing. If we add to this the fact that the modern optimisation of topology is also all the more capable of delivering a form, which are suitable for classic production (for example: casting, forging, welding), it becomes clear that the optimisation of topology has, or sooner or later, will very much return to the early phases of planning the supporting structure of parts.
3D modelling
Fundamental principles of 3D modelling
3D modelling, as a part of computer graphics, is closely connected with mathematics, above all, linear algebra. It has to do with the process of creating a mathematical representation of a three-dimensional object. This process enables the computer to show represented objects on a two-dimensional screen which we call 3D modelling. 3D modelling is founded on mathematics and physics.
Creating mathematical representations of three-dimensional objects, or 3D modelling, can be achieved in two ways: with the use of tools in programs for modelling or direct with programming and the use of mathematical equations. The use of such intended tools is a more simplified approach, as it enables the designer significantly greater control over the shape of the model. Such programs are written in the background by equations which suit the model on the screen, while designers take care of nothing more than the look of the model.
During the use of such programs, the computer shows a visual representation of our objects, while in the background it operates with a large number of data, typically stored in matrixes. The result of this kind of creating we call a 3D model.
Modelling operations
The 3D model is built from a grid, which consists of points and lines that together form a polygon grid. The grid can be changed directly by controlling the points and indirectly the edges (lines) and polygons in different ways. Points, edges and polygons can be moved and extended in space, edges and polygons can also be scaled and rotated. Changing a model is called object manipulation and is achieved through modelling operations. Modelling operations include translation (parallel shift), rotation, and scaling (resizing). We know even more modelling operations, all of which have in common that we can combine them and use several operations on the object at the same time – this is called a composite of operations.
Some of the basic modelling operations are: Boolean operations, extruding, edge looping, subdivisional surfaces (SubD), bevelling and many others…
Modelling approaches
Modelling is an industry where the same results (3D models) can be created using different techniques. Each has its advantages and disadvantages, which makes it useful to know as many techniques as possible and adapt to the choice of technique and to the type of model. This can often save us a lot of time or improve the accuracy and detail of the model.
The oldest approach that is still widely used is the build out or edge-by-edge approach. Polygon modelling involves manipulating one of the basic characters, usually a cube or sphere, using basic operations of displacing and dividing surfaces. We also know the use of NURBS curves (NURBS – Non-Uniform Rational Basis Spline are mathematically defined curves determined by order, a set of weighted (or unweighted) control points and knot vector) and digital sculpture, a method that is very similar to traditional sculpture. With the help of various tools, the designer transforms one of the basic shapes, which typically has a large number of polygons, which gives him great control over the processing of the shape.
Topology in 3D modelling
The definition of topology
A topology is the addition or subtraction of material within the boundaries where the material may be located. The task of the mathematical algorithm or the optimiser is to determine where the actual material should be and where it should not. Topology optimisation brings great help and advantage to engineers in developing and designing optimal structural elements. The structures have a lower mass, a high stiffness, minimum stress levels and do not contain stress concentrations.
The topology can be used in all industries and is mainly present in the automotive, aerospace weapons and outer space industries.
A program for the optimisation of topology
Topology optimization program – ProTOp, is a stand-alone high-performance computer program made on the basis of its own finite elements specialized in topology optimization. The input to the program are FNF, INP, GEO, and DAT files made with PTC® Creo®, Simulia® Abaqus, SolidWorks® Simulation, and Siemens NX ™. It is characterized by:
- the simple use of an interface,
- the fast configuration of solid, shell and lattice structures and immediate optimisation,
- excellent results and surface smoothing tools – optimized structures are suitable for 3D printing and other manufacturing processes
The optimisation process includes the production of a 3D CAD model, a numerical FEM model and the implementation of topological optimisation. The result of topological optimisation with ProTOp are structures suitable for 3D printing and other manufacturing processes.
Topology in 3D modelling
In modelling, mesh topology indicates the way in which a 3D model is constructed, how polygons are arranged and interconnected. The layout and flow of polygons is very important if we want to add materials to the model. If the arrangement of the polygons is inappropriate, some parts of the texture on the model may stretch or shrink too much when the materials are applied, and even tear when the model is deformed.
Topology optimisation
Topology optimisation is increasingly becoming a necessary component, especially in the design of load-bearing structural parts. The design of load-bearing parts is an increasingly sought-after and demanding task of engineers, the reasons for which are the increased requirements for mechanical response and the load-bearing capacity of the element, long service life, mass of material used for manufacturing and of course the manufacturing process. Fortunately, the development of software also follows the increase of the mentioned requirements.
If engineers are to be successful, they must now, in addition to all other skills, use state-of-the-art tools to design such parts, taking into account efficient construction and subsequent use. These include topology optimisation. The concept in the construction of load-bearing parts is e.g. weight reduction at the same or even greater load on the individual piece and consequently the product.
The optimisation of topology of load-bearing mechanical parts
In the field of development of optimization methods, the optimization of the topology of load-bearing mechanical parts is currently by far the most important. Namely, topology optimization can, compared to other optimization procedures, bring the most benefits.
With the 3D printing process, we can create any shape, and the range of available printing materials is wider every day. This fact opens a wide way for the application of procedures to optimize the topology of load-bearing parts. In fact, it should not be avoided at all, the fact is that printed materials are quite sensitive to stress concentrations, which leads to the appearance of cracks, which in turn leads to the collapse of the mechanical part. To reduce failure, it is first and foremost necessary to ensure that the load-bearing part is under load without stress concentrations.
Problems often arise due to the poor knowledge of optimisation procedures and the incorrect formulation of the optimisation task. Any irregularity in the formulation of the task can lead to seemingly optimal solutions, which in reality lead to failures.
Topology optimisation can significantly improve and facilitate the design processes of load-bearing parts of structures, but it should be noted that errors in the description of the optimisation task can quickly lead us to a result that will not be able to withstand actual loads. Careful preparation of the model is extremely important here.
Topology optimisation is the addition or subtraction of material within boundaries or the domain where the material can be located. The task of the mathematical algorithm or the optimiser is to determine where the actual material should be and where it should not. Optimisation is performed based on prescribed loads and boundary conditions. The benefits of optimised load-bearing parts are significant, as they are lighter and with optimal weight, more rigid, without stress concentrations and more resistant to fatigue.
Author of the article: Dr. Boštjan Harl, Engg.
Source: Carli: Fundamental principles of 3D modelling, Matrika 2016
