H Herm Hofmeyer

New prediction model for failure of steel sheeting subject to concentrated load (web crippling) and bending

Abstract Current design rules for steel sheeting do not give adequate insight in the sheetings structural behaviour and are not always accurate. The current rules use three concepts: ultimate bending moment; ultimate concentrated load; and interaction. This paper presents a new analytical model to predict the ultimate load of first-generation sheeting under practical loading conditions. These practical conditions are defined by the ratios between bending moment and concentrated load as occurring in practice. Comparisons between the new model and experiments indicate that the new model reaches approximately the same accuracy as the design rules. The new model provides more insight in the structural behaviour of the sheeting and uses only one concept for determining failure. The new model is based on two existing models. Namely an analytical model developed in 1995 by Vaessen (On the elastic web crippling stiffness of thin-walled cold-formed steel sections, Graduate Thesis TUE-BKO-95-17, Eindhoven University of Technology, The Netherlands) to predict the local web crippling deformation and a solution of Marguerres (Zur Theorie der gekrummter Platte grosser Formanderung. Proc. Fifth. Int. Congress Appl. Mech., p. 93) simultaneous differential plate equations included in a book by Murray (Introduction to the Theory of Thin-walled Structures, Oxford Engineering Science Series 13, Clarendon Press, Oxford).

Combined web crippling and bending moment failure of first-generation trapezoidal steel sheeting

Current design rules for cold-formed trapezoidal sheeting, which predict sheeting failure for an interior support, do not provide sufficient insight into the sheeting behaviour, and can differ up to 40% in their predictions. To develop a new design rule, this article presents new experiments in which first-generation sheeting behaviour is studied for practical situations. The experiments show that after ultimate load, three different post-failure modes arise. Finite element models were used to simulate the experiments. Studying stress distributions with finite element simulations, it can be seen that there are only two ultimate failure modes at ultimate load. One of these ultimate failure modes is probably not relevant for practice. A mechanical model has been developed for the other ultimate failure mode. This model performs as well as the current design rules, and it provides insight into the sheeting behaviour.

Coevolutionary and genetic algorithm based building spatial and structural design

Abstract In this article, two methods to develop and optimize accompanying building spatial and structural designs are compared. The first, a coevolutionary method, applies deterministic procedures, inspired by realistic design processes, to cyclically add a suitable structural design to the input of a spatial design, evaluate and improve the structural design via the finite element method and topology optimization, adjust the spatial design according to the improved structural design, and modify the spatial design such that the initial spatial requirements are fulfilled. The second method uses a genetic algorithm that works on a population of accompanying building spatial and structural designs, using the finite element method for evaluation. If specific performance indicators and spatial requirements are used (i.e., total strain energy, spatial volume, and number of spaces), both methods provide optimized building designs; however, the coevolutionary method yields even better designs in a faster and more direct manner, whereas the genetic algorithm based method provides more design variants. Both methods show that collaborative design, for example, via design modification in one domain (here spatial) to optimize the design in another domain (here structural) can be as effective as monodisciplinary optimization; however, it may need adjustments to avoid the designs becoming progressively unrealistic. Designers are informed of the merits and disadvantages of design process simulation and design instance exploration, whereas scientists learn from a first fully operational and automated method for design process simulation, which is verified with a genetic algorithm and subject to future improvements and extensions in the community.

Spatial to kinematically determined structural transformations

To understand the building design process and to help designers involved, the idea of a research engine has been developed: In this engine cyclic transformations take place between spatial and structural building designs. With this engine, a design process can be studied closely and subjected to improvement, and designers can be supported. To develop the engine, in this paper a part of it is studied, namely the transformation from spatial to structural design, which can be divided into four sub transformations: (1) from spatial design to structural topology; (2) from structural topology to mechanical model; (3) from mechanical model to finite element model; (4) from finite element model to design recommendations. For the first sub transformation, two different techniques are presented: Spatial-Structural Transformation Rules and Element Selection. For the second sub transformation, also two techniques are presented: Element Approach and System Approach. Where possible, data models in EXPRESS and process models in IDEF0 are used. For the third and fourth sub transformation, new procedures have been developed using data models in EXPRESS. To test the data and process models for all four sub transformations, a simplified two-storey building, derived from a real six-storey apartment building, is used as case study. It can be concluded that the developed sub transformations function well, related to their application in the research engine, and that their development raises new research questions that have to be solved in the near future.

Automated design studies

This paper presents the development of a virtual toolbox for the study of spatial-structural design processes. It will be able to transform a spatial design into a structural design. After structural optimisation, the structural design is interpreted as a spatial design. This spatial design is then modified to comply with the initial design requirements after which a new cycle starts. The transformation and optimisation processes within the toolbox can be altered, allowing automated design studies to be carried out. In this article, two processes for the structural optimisation are investigated to determine which is most suitable for specific conditions. These two processes are: (a) Topology Optimisation applied to complete structural systems for buildings; (b) Evolutionary Structural Optimisation for which only the first step is used. It can be concluded that: (a) although Topology Optimisation is formally more correct, One-Step Evolutionary Structural Optimisation will yield almost the same qualitative results, (b) quantitatively the methods cannot be compared exactly, however, it is likely that Topology Optimisation results in more efficient structures and (c) Topology Optimisation always leads to stable structures, whereas One-Step Evolutionary Structural Optimisation may yield a singular stiffness matrix, although this has no influence on the spatial design derived from the optimised structural design. It is intended to utilise the optimisation techniques in the virtual toolbox leading to design studies and to transcend additional transformation and optimisation processes in the virtual tool box via formal description. Fields of application are the academic study of spatial-structural design processes (i.e. design theory), the optimisation of all possible structural design types (i.e. design optimisation), and the generation of design instances (i.e. generative design).

An automated stabilisation method for spatial to structural design transformations

A spatial-structural design process can be investigated via a so-called research engine, in which a spatial design is transformed into a structural design and vice versa. During the transformation from a spatial into a structural design, it is necessary to obtain a stable structural model, so that a structural analysis can be carried out. This article presents four methods to automate the (normally carried out intuitively) stabilisation process, using data related to a structural designs geometry and its instability modes. The methods all use the null space and associated null vectors of the structural stiffness matrix. Then each null vector is resolved by either (a) rod addition, (b) plane addition, (c) hinge fixation by single rod substitution, or (d) hinge fixation by coupled rod substitution. The methods have been implemented in C++ and several test cases have been carried out. The test cases explain why (a) rod addition provides the most realistic solutions, (b) if several methods are used subsequently for one problem, superfluous elements are inevitable, (c) there is a serious influence on the performance for various systems of key point numbering, (d) the efficiency of the methods is not optimal and may be improved by some suggested strategies.

Multicriteria building spatial design with mixed integer evolutionary algorithms

This paper proposes a first step towards multidisciplinary design of building spatial designs. Two criteria, total surface area (i.e. energy performance) and compliance (i.e. structural performance), are combined in a multicriteria optimisation framework. A new way of representing building spatial designs in a mixed integer parameter space is used within this framework. Two state-of-the-art algorithms, namely NSGA-II and SMS-EMOA, are used and compared to compute Pareto front approximations for problems of different size. Moreover, the paper discusses domain specific search operators, which are compared to generic operators, and techniques to handle constraints within the mutation. The results give first insights into the trade-off between energy and structural performance and the scalability of the approach.

A super-structure based optimisation approach for building spatial designs

Building design can be supported effectively by computer-aided design exploration. This paper investigates optimisation based on a mixed-integer super-structure representation of the search space of building spatial designs. It can take into account parametric as well as topological variations. In the suggested super-structure – the so-called supercube representation – discrete and continuous variables determine the existence, respectively, dimensioning of spaces of the building spatial design. Constraints are formulated as closed form equations and can be used to numerically assess the feasibility of designs. A population-based constraint-handling evolutionary strategy is developed. In the constraint handling repair and penalty methods are combined in a domain specific way. The method is tested on different search space sizes and first promising results are reported.

Pre-processing parallel and orthogonally positioned structural design elements to be used within the finite element method

Abstract Two methods for pre-processing of (parallel and orthogonal positioned) structural design elements, to be used for specifying kinematically undetermined behaviour within the finite element method, are presented. One method is based on first checking line–line combinations, using a (2D) projection technique, followed by investigating line–area combinations employing a line–line combination related technique. These procedures (line–line and line–area) are repeated until convergence occurs. The method is finalised by pattern recognition to find all new areas within the original areas. The second method is also based on (iteratively) checking line–line combinations and line–area combinations but now line–line combinations are studied using a line–area intersection technique and line–area combinations are investigated with a technique that makes (expensive) pattern recognition superfluous. Both methods are implemented in C++ and are compared for correctness and efficiency by using academic and building design examples. It can be concluded that the second method seems an appropriate candidate for further implementation.

Toolbox for super-structured and super-structure free multi-disciplinary building spatial design optimisation

Abstract Multi-disciplinary optimisation of building spatial designs is characterised by large solution spaces. Here two approaches are introduced, one being super-structured and the other super-structure free. Both are different in nature and perform differently for large solution spaces and each requires its own representation of a building spatial design, which are also presented here. A method to combine the two approaches is proposed, because the two are prospected to supplement each other. Accordingly a toolbox is presented, which can evaluate the structural and thermal performances of a building spatial design to provide a user with the means to define optimisation procedures. A demonstration of the toolbox is given where the toolbox has been used for an elementary implementation of a simulation of co-evolutionary design processes. The optimisation approaches and the toolbox that are presented in this paper will be used in future efforts for research into- and development of optimisation methods for multi-disciplinary building spatial design optimisation.