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36-430: Z88 may refer to: Z88 FEM software , a finite element software package Cambridge Z88 , a 1988 portable Z80-based computer Vektor Z88 , a handgun [REDACTED] Topics referred to by the same term This disambiguation page lists articles associated with the same title formed as a letter–number combination. If an internal link led you here, you may wish to change

72-422: A Windows user interface with context-sensitive online help. Handbooks are available, demonstrating the use of Z88 and Z88Aurora, using examples. The Freeware is available for Windows, Linux and OS X. Topology optimization is done by optimizing an existing structure towards a given target function by changing its topology class within a pre-defined space. By removing material in suitable places an optimal structure

108-405: A discrete sense is done by discretizing the design domain into finite elements. The material densities inside these elements are then treated as the problem variables. In this case material density of one indicates the presence of material, while zero indicates an absence of material. Owing to the attainable topological complexity of the design being dependent on the number of elements, a large number

144-533: A mapped mesher for superelement structures (hexahedrons, shells, etc.), a shell thickener that creates column shells from 2D shell elements and a trimming function serve to refine the model. The set management enables an easy selection of surfaces, nodes and elements to apply boundary conditions, define materials, etc. The material database contains 52 pre-defined materials and is editable and can be extended easily. Various boundary conditions such as forces, displacements, pressure and thermal conditions can be applied using

180-399: A problem is still infeasible owing to issues such as: Some techniques such as filtering based on image processing are currently being used to alleviate some of these issues. Although it seemed like this was purely a heuristic approach for a long time, theoretical connections to nonlocal elasticity have been made to support the physical sense of these methods. Fluid-structure-interaction

216-477: A program to calculate point concentrated and linear loads on glass panes in building construction. Routines have been implemented to determine the Young's modulus and flexural strength of wood and a sub-application has been developed to calculate pressure vessels. Examples of companies using Z88 are The availability of the source code and thus the transparency of applied algorithms and material models make Z88 ideal as

252-430: A reference software for commercial tools such as NASTRAN and ABAQUS . Topology optimization Topology optimization is a mathematical method that optimizes material layout within a given design space, for a given set of loads , boundary conditions and constraints with the goal of maximizing the performance of the system. Topology optimization is different from shape optimization and sizing optimization in

288-439: A total of 25 different element types, including 2D elements (truss, beam, plane stress elements, shaft elements, torus elements) and 3D elements (truss, beam, linear and quadratic tetrahedrons and hexahedrons ). Two open source meshers (TetGen, by Dr. Hang Si (WIAS Berlin) and NETGEN, by Prof. Joachim Schöberl (TU Wien)) generate tetrahedron meshes. A tetrahedrons refiner for existing tetrahedrons meshes (linear and quadratic),

324-406: A wide range of applications in aerospace, mechanical, bio-chemical and civil engineering. Currently, engineers mostly use topology optimization at the concept level of a design process . Due to the free forms that naturally occur, the result is often difficult to manufacture. For that reason the result emerging from topology optimization is often fine-tuned for manufacturability. Adding constraints to

360-544: Is a strongly coupled phenomenon and concerns the interaction between a stationary or moving fluid and an elastic structure. Many engineering applications and natural phenomena are subject to fluid-structure-interaction and to take such effects into consideration is therefore critical in the design of many engineering applications. Topology optimisation for fluid structure interaction problems has been studied in e.g. references and. Design solutions solved for different Reynolds numbers are shown below. The design solutions depend on

396-483: Is achieved. Depending on the goal of the topology optimization two different methods can be chosen: The OC method produces a design suggestion that features maximal stiffness in relation to a previously defined relative volume. The SKO process optimizes for maximum strength. The TOSS algorithm was specially developed by the development team at the University of Bayreuth and can be understood as an advancement of

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432-428: Is at this point that the exact model and design variables for the optimization process are defined. Not only the target function but also the boundary conditions and restrictions are defined here. The optimization problem is solved by an algorithm that iterates variations of the design variables. The result is an improved draft model, that goes through the same process until an optimal draft, the so-called design suggestion

468-404: Is created. The goal of topology optimization is the automatic creation of an optimal structure under defined applied forces and boundary conditions within the virtual product development process. A draft model provides the basis. Displacements, stresses and natural frequencies and oscillations are computed via a structural analysis and will be taken into consideration by the optimization process. It

504-405: Is in reality a cost factor, as we would not want to spend a lot of money on the material. To obtain the total material utilized, an integration of the selection field over the volume can be done. Finally the elasticity governing differential equations are plugged in so as to get the final problem statement. subject to: But, a straightforward implementation in the finite element framework of such

540-400: Is possible to smooth the resulting structure and export it as STL to ensure direct reuse of the optimized part in other programs. There is also a direct interface to Z88Aurora. Z88 has been used to educate engineering students at the University of Bayreuth since 1998. The possibility of manual creation of the structure and the application of boundary conditions enables a simple visualization of

576-639: Is preferred. Large numbers of finite elements increases the attainable topological complexity, but come at a cost. Firstly, solving the FEM system becomes more expensive. Secondly, algorithms that can handle a large number (several thousands of elements is not uncommon) of discrete variables with multiple constraints are unavailable. Moreover, they are impractically sensitive to parameter variations. In literature problems with up to 30000 variables have been reported. The earlier stated complexities with solving topology optimization problems using binary variables has caused

612-484: The Lanczos procedure. The results are visualized using the post-processor. It is possible to filter results or clip the part to view only the relevant sections. Specific results can be exported to text or CSV format and the analysis function permits the display of results pertaining to a single node. Moreover, the deformed structure can be used in other applications by exporting it to an STL file. The software comes with

648-548: The OC method. It is a hybrid process of OC and a so-called SKO method (Soft Kill Option) and uses the optimal stiff structure resulting from the OC method and uses it as a basis to create a stress-optimized design suggestion. To do so material is added in overstressed areas and removed in understressed areas. The determined design proposal is displayed in the postprocessor. For example, the user can look at different iterations and vary presentation limits. In addition, since Z88Arion V2, it

684-574: The Zonguldak Karaelmas Üniversitesi. Additionally Z88 has been used for degree theses at the Universities of Darmstadt, Hamburg-Harburg, Munich, Karlsruhe, Bern and Beijing (among others). Furthermore, there are two textbooks using Z88. Finite Elemente Analyse for Ingenieure: Eine leicht verständliche Einführung has sold over 6000 copies. This textbook is designed for entry-level users of finite element analysis and useas Z88 to let

720-411: The community to search for other options. One is the modelling of the densities with continuous variables. The material densities can now also attain values between zero and one. Gradient based algorithms that handle large amounts of continuous variables and multiple constraints are available. But the material properties have to be modelled in a continuous setting. This is done through interpolation. One of

756-786: The conversion of thermal energy into electric energy and the Peltier effect concerns the conversion of electric energy into thermal energy. By spatially distributing two thermoelectric materials in a two dimensional design space with a topology optimisation methodology, it is possible to exceed performance of the constitutive thermoelectric materials for thermoelectric coolers and thermoelectric generators . The current proliferation of 3D printer technology has allowed designers and engineers to use topology optimization techniques when designing new products. Topology optimization combined with 3D printing can result in less weight, improved structural performance and shortened design-to-manufacturing cycle. As

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792-406: The derivatives of the objective function are non-zero when the density becomes zero. The higher the penalisation factor, the more SIMP penalises the algorithm in the use of non-binary densities. Unfortunately, the penalisation parameter also introduces non-convexities. There are several commercial topology optimization software on the market. Most of them use topology optimization as a hint how

828-435: The fluid flow with indicate that the coupling between the fluid and the structure is resolved in the design problems. Thermoelectricity is a multi-physic problem which concerns the interaction and coupling between electric and thermal energy in semi conducting materials. Thermoelectric energy conversion can be described by two separately identified effects: The Seebeck effect and the Peltier effect. The Seebeck effect concerns

864-444: The following: Evaluating u ( ρ ) {\displaystyle \mathbf {u(\rho )} } often includes solving a differential equation. This is most commonly done using the finite element method since these equations do not have a known analytical solution. There are various implementation methodologies that have been used to solve topology optimization problems. Solving topology optimization problems in

900-418: The formulation in order to increase the manufacturability is an active field of research. In some cases results from topology optimization can be directly manufactured using additive manufacturing ; topology optimization is thus a key part of design for additive manufacturing . A topology optimization problem can be written in the general form of an optimization problem as: The problem statement includes

936-754: The function of FEM software. Due to the open file sources the software can be used for research purposes in FE areas and can be modified to suit individualized needs. Among others, Z88 is used for research and teaching at the University Ravensburg-Weingarten , the University of Ioannina , the Penn State University , the Universidad de Buenos Aires , the University of Cagliari , the University of Maribor , and at

972-457: The graphical user interface. The solver computes displacements, stresses, temperatures and nodal forces depending on the selected computation module. Four numerical solvers are available for the linear finite element analysis: Stationary thermal or thermomechanical calculations use the iterative solvers or the direct multicore solver. Nonlinear calculations are done by applying a special iterative solver. The natural frequency simulation uses

1008-400: The link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Z88&oldid=1195264245 " Category : Letter–number combination disambiguation pages Hidden categories: Short description is different from Wikidata All article disambiguation pages All disambiguation pages Z88 FEM software The software

1044-496: The material to the scalar selection field. The value of the penalisation parameter p {\displaystyle p} is generally taken between [ 1 , 3 ] {\displaystyle [1,\,3]} . This has been shown to confirm the micro-structure of the materials. In the SIMP method a lower bound on the Young's modulus is added, E 0 {\displaystyle E_{0}} , to make sure

1080-483: The most implemented interpolation methodologies is the Solid Isotropic Material with Penalisation method (SIMP). This interpolation is essentially a power law E = E 0 + ρ p ( E 1 − E 0 ) {\displaystyle E\;=\;E_{0}\,+\,\rho ^{p}(E_{1}-E_{0})} . It interpolates the Young's modulus of

1116-401: The optimal design should look like, and manual geometry re-construction is required. There are a few solutions which produce optimal designs ready for Additive Manufacturing. A stiff structure is one that has the least possible displacement when given certain set of boundary conditions. A global measure of the displacements is the strain energy (also called compliance ) of the structure under

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1152-406: The prescribed boundary conditions. The lower the strain energy the higher the stiffness of the structure. So, the objective function of the problem is to minimize the strain energy. On a broad level, one can visualize that the more the material, the less the deflection as there will be more material to resist the loads. So, the optimization requires an opposing constraint, the volume constraint. This

1188-509: The sense that the design can attain any shape within the design space, instead of dealing with predefined configurations. The conventional topology optimization formulation uses a finite element method (FEM) to evaluate the design performance. The design is optimized using either gradient-based mathematical programming techniques such as the optimality criteria algorithm and the method of moving asymptotes or non gradient-based algorithms such as genetic algorithms . Topology optimization has

1224-517: The user follow the examples shown in the book on his own system. The book Maschinenelemente - Funktion, Gestaltung und Berechnung by Decker (19th edition) uses practical applications with Z88 to teach the calculation of machine elements with finite element analysis. Due to the Open Source approach many applications use the Z88 solver, its plot output, etc. Among other things Z88 has been adapted into

1260-567: Was developed by Frank Rieg, a professor for engineering design and CAD at the University of Bayreuth . Originally written in FORTRAN  77, the program was ported to the programming language C in the early 1990s. There are two programs for finite element analysis: Since 2014 two Android Apps are also available: The product family is supported by a software for topology optimization since 2016: Z88Aurora's current version contains several computation modules: Regardless of what module

1296-730: Was selected the finite element analysis using Z88Aurora can be divided into three areas: pre-processor, solver (processor) and post-processor. The pre-processor builds the FE model. It is possible to either build the structure directly inside the software by using Z88Aurora's tools and using structural elements such as trusses and beams or a model can be imported from several file formats. Geometries can be imported from STEP files (*.STP), STL files in ASCII or binary format (*.STL) or Autocad files (*.DXF), while FE structure data can be imported from NASTRAN files (*.NAS), ABAQUS files (*.INP), ANSYS files (*.ANS) or COSMOS files (*.COS). Z88Aurora contains

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