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- Gustafsson, Erik, et al.
(författare)
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Residual stresses in a stress lattice : experiments and finite element simulations
- 2009
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Ingår i: Journal of Materials Processing Technology. - : Elsevier. - 0924-0136 .- 1873-4774. ; 209:9, s. 4320-4328
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Tidskriftsartikel (refereegranskat)abstract
- In this work residual stresses in a stress lattice are studied. The residual stresses are both measured and simulated. The stress lattice is casted of low alloyed grey cast iron. In fact, nine similar lattices are casted and measured. The geometry of the lattice consists of three sections in parallel. The diameter of the two outer sections are thinner than the section in the middle. When the stress lattice cools down, this difference in geometry yields that the outer sections start to solidify and contract before the section in the middle. Finally, an equilibrium state, with tensile stresses in the middle and compressive stresses in the outer sections, is reached. The thermo-mechanical simulation of the experiments is performed by using Abaqus. The thermo-mechanical solidification is assumed to be uncoupled. First a thermal analysis, where the lattice is cooled down to room temperature, is performed. Latent heat is included in the analysis by letting the fraction of solid be a linear function of the temperature in the mushy zone. After the thermal analysis a quasi-static mechanical analysis is performed where the temperature history is considered to be the external force. A rate independent J2-plasticity model with isotropic hardening is considered, where the material data depend on the temperature. Tensile tests are performed at room temperature, 200°C, 400°C, 600°C and 800°C in order to evaluate the Young´s modulus, the yield strength and the hardening accurate. In addition, the thermal expansion coefficient is evaluated for temperatures between room temperature and 1000°C. The state of residual stresses is measured by cutting the mid section or the outer section. The corresponding elastic spring-back reveals the state of residual stresses. The measured stresses are compared to the numerical simulations. The simulations show good agreement with the results from the experiments.
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| 4. |
- Hofwing, Magnus, 1982-, et al.
(författare)
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D-optimality of non-regular design spaces by using a Bayesian modification and a hybrid method
- 2010
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Ingår i: Structural and multidisciplinary optimization (Print). - : Springer. - 1615-147X .- 1615-1488. ; 42:1, s. 73-88
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Tidskriftsartikel (refereegranskat)abstract
- In this work a hybrid method of a genetic algorithm and sequential linear programming is suggested to obtain a D-optimal design of experiments. Regular as well as non-regular design spaces are considered. A D-optimal design of experiments maximizes the determinant of the information matrix, which appears in the normal equation. It is known that D-optimal design of experiments sometimes include duplicate design points. This is, of course, not preferable since duplicates do not add any new information to the response surface approximation and the computational effort is therefore wasted. In this work a Bayesian modification, where higher order terms are added to the response surface approximation, is used in case of duplicates in the design of experiments. In such manner, the draw-back with duplicates might be eliminated. The D-optimal problem, which is obtained by using the Bayesian modification, is then solved by a hybrid method. A hybrid method of a genetic algorithm that generates a starting point for sequential linear programming is developed. The genetic algorithm performs genetic operators such as cross-over and mutation on a binary version of the design of experiments, while the real valued version is used to evaluate the fitness. Next, by taking the gradient of the objective, a LP-problem is formulated which is solved by an interior point method that is available in Matlab. This is repeated in a sequence until convergence is reached. The hybrid method is tested for four numerical examples. Results from the numerical examples show a very robust convergence to a global optimum. Furthermore, the results show that the problem with duplicates is eliminated by using the Bayesian modification.
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| 7. |
- Hofwing, Magnus
(författare)
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Design of Experiments - A- D- I- S-optimality
- 2010
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Ingår i: Proceedings of the 2nd International Conference on Engineering Optimization (EngOpt2010).
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Konferensbidrag (refereegranskat)abstract
- A metamodel approximates an original model with a model that is more efficient and yields information about the response. Response surfaces and Kriging approximations are such metamodels. A metamodel is based on evaluations of the original function at some design points, where the choice of design points is crucial. The design points constitute the design of experiments (DoE). There are many methodologies of how to chose the DoE. In this work A-, D-, I- and S-optimal DoEs are generated and evaluated. The optimal DoEs are obtained by solving the following mathematical optimization problems:A-otimality. Minimize the average variance of the model coefficient estimates.D-otimality. Minimize the generalized variance of the model coefficient estimates.I-otimality. Minimize the average of the expected variance (taken as an integral)over the region of prediction.S-otimality. Maximize the geometric mean of the distances between nearest neighborsof the design points.The optimization problems are solved by a hybrid method which consists of a genetic algorithm and sequential linear programming. The different optimality criteria are evaluated for a number of test cases in order to show the characteristics of each criteria. Regular as well as non-regular design spaces are considered. Furthermore, Kriging approximations of the well known Rosenbrock’s banana function are generated to evaluate the accuracy of a resulting metamodel based on the different DoEs. Results from the test cases show that D-optimal DoEs tend to place more design points close to the boundary of the design space compared to A- and I-optimality. It is also shown that A- D- and I-optimal DoEs often include duplicate design points which is not beneficial for a deterministic response, but might be beneficial for non-deterministic responses. Concerning S-optimal DoEs the design points are evenly distributed over the entire design space and no duplicates occur. Furthermore, the S-optimal DoE generates the best fitted Kriging approximation of the Rosenbrock’s banana function.
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| 9. |
- Hofwing, Magnus, 1982-, et al.
(författare)
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Optimal Polynomial Regression Models by using a Genetic Algorithm
- 2011
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Ingår i: Proceedings of the Second International Conference on Soft Computing Technology in Civil, Structural and Environmental Engineering. - Stirlingshire : Civil-Comp Press. - 9781905088492 - 9781905088485
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Konferensbidrag (övrigt vetenskapligt/konstnärligt)abstract
- Different regression models are commonly used to approximate the behavior of an unknown response in a given design domain. The regression models are usually obtained from a design of experiments, the corresponding responses and the constitution of the regression model. In this work a new approach is proposed, where the constituents of a polynomial regression model are of arbitrary order. A genetic algorithm is used to find the optimal terms to be included in the so-called optimal polynomial regression model. The objective for the genetic algorithm is to minimize the sum of squared errors of the predicted responses. In practice the genetic algorithm generates an optimal set of exponents of the design variables for the specified number of terms in the regression model, where each term is a product of a regression coefficient and the design variables. Several example problems are presented to show the performance and accuracy of the optimal polynomial regression model. Results show an improved performance for optimal polynomial regression models compared to traditional regression models.
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