The aim of this paper is to introduce an efficient and accurate new approach called Monte Carlo and Kriging (MCK) to robust topology optimization. The objective is to minimize the expected value of ''compliance'' under concentrated loading uncertainty. The loading uncertainty may occur in magnitude, direction and/or position. The Monte Carlo simulation method and Kriging model are used to evaluate the objective function. To evaluate the expected value of ''compliance'' the probabilistic problem is transformed into a multiple loading deterministic one using of Monte Carlo method but with a reduced evaluations number of simulation model. A small sample obtained with a Latin Hypercube is used to build a Kriging model of the simulation model. This is utilized to estimate the ''compliance'' in those points used by Monte Carlo simulation method. Two problems are solved to demonstrate the efficiency and accuracy of the approach. The examples are solved again using a standard Monte Carlo simulation to check the proposed approach.
Abstract The aim of this paper is to introduce an efficient and accurate new approach called Monte Carlo and Kriging (MCK) to robust topology optimization. The objective is to minimize [...]
The probabilistic analysis of the seismic performance of a structure requires quantifying the uncertainties of the involved variables and parameters, including the seismic action and mechanical properties of its elements. In this article, the seismic performance of high-rise, mid-rise and low-rise of steel buildings, subjected to long duration seismic actions like those of Mexico City, is analyzed. The analysis is conducted by using a probabilistic approach. The seismic actions are selected to be compatible with the design spectra of the Mexican seismic code for soft soils and long duration earthquakes, characteristic for this region. The dynamic analyses are performed by using Monte Carlo simulations. The strength and ductility of the beams and columns are considered random variables; the seismic actions are also modelled in a probabilistic way. The damage index of Park and Ang is used. The results show that the uncertainties expected in the response are significant, being the randomness of the seismic action the main cause. From the comparison between the mean values of the probabilistic approach and those corresponding to the deterministic case, a good consistency of the result obtained for low-rise and mid-rise buildings is observed. Nevertheless, the consistency is lower in the case of high-rise buildings. The analyzed low-rise and mid-rise buildings show a good seismic performance to seismic actions, but the high-rise buildings show slight or moderate damage. It is concluded that the probabilistic approach provides a more complete information on the structural response.
Abstract The probabilistic analysis of the seismic performance of a structure requires quantifying the uncertainties of the involved variables and parameters, including the seismic [...]
Several residential, commercial and industrial applications have their efficiency increased when a thermal energy storage system is incorporated. The PCMs (Phase Change Materials), due to their high latent heat of fusion, are materials that represent a viable alternative to the implementation of thermal energy storage systems. This paper presents a numerical study of RT (Rubitherm Technologies GmbH) PCMs family fusion process in cylindrical cavities. The study was conducted through a CFD ''(''Computational Fluid Dynamics) numerical simulation, with ANSYS Fluent software. The numeric model adopted is two-dimensional and has been validated with numerical and experimental results of literature, achieving a good approximation. For PCMs here studied, increasing the temperature from 10 ''<sup>o</sup>C'' to 20 ''<sup>o</sup>C'' and 10 ''<sup>o</sup>C'' to 30 ''<sup>o</sup>C'', above the phase change temperature, for liquid fractions between 0.4 and 0.8, the average reduction of fusion time is approximately 55.8% and 71.8 %, respectively.
Abstract Several residential, commercial and industrial applications have their efficiency increased when a thermal energy storage system is incorporated. The PCMs (Phase Change Materials), [...]
In this paper an automatic remeshing algorithm of triangular finite elements is presented. It is well known that the element sizes of the mesh play an important role in modeling the continuum, particularly when notable material properties differences exist in contiguous areas of the medium. In such cases, the mesh must be fine enough in such areas in order to obtain reliable results. Therefore, in this paper is advanced an algorithm to carry out automatic remeshing of local areas where the “remeshing” criteria is activated to refine the mesh accordingly. Herein the proposed algorithm integrated into a two dimensional finite element computer program is used to analyze a classical geotechnical problem to show the importance of locally refining the mesh and to demonstrate that regardless of the geometric characteristics of the initial mesh, the algorithm yields practically equal results. Computations with the proposed method are compared with the corresponding close form solutions, whenever available, to show the usefulness and reliability of the remeshing algorithm. Furthermore, to show the algorithm’s versality, the initial loading boundary conditions considered for the cases included in this paper are modified in order to show how the automatic local remeshing is capable of adapting the initial mesh configuration into a new one as a function of the new boundary conditions. As shown in the paper, the final resulting meshes for both load boundary conditions considered are appreciably dissimilar from each other, which leads to somehow different results.
Abstract In this paper an automatic remeshing algorithm of triangular finite elements is presented. It is well known that the element sizes of the mesh play an important role in modeling [...]
Robust topology optimization of continuum structures using Monte Carlo method and Kriging models 
489New York Institute of Technology
