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## SIAM Review

Share full text access. Please review our Terms and Conditions of Use and check box below to share full-text version of article. Abstract This article reviews the application of probability theory and statistical analysis to wind loading of structures, a field which has developed considerably during the last 30 years. Citing Literature. Volume 1 , Issue 2 January Pages Related Information. Close Figure Viewer.

Browse All Figures Return to Figure. Previous Figure Next Figure. The optimisation problem is considered with 1, 2 and 4 design variables. Figure 2 shows the distribution of the design variables in the finite element mesh. Clamped in 4 sides. The results of the optimization are shown in Table 1 and Figure 4.

Table 1 presents the results of the optimization problem with 1, 2 and 4 variables and reduction of the objective function when there is an increase in the number of project variables. With the increase in design variables above, 4 had no significant reduction in the objective function. The observation of these results indicates that the increase in the number of design variables leads to a diminishing value of the objective function, which is to be expected.

In the sequel, the equivalent probabilistic optimization is performed. Now the problem is defined as. To attain consistence, the value of the constraint is calculated from an analysis of the results obtained with the final values of the design variables in the deterministic optimization and the load is given from the Fourier transform Figure 5 of the load considered in the deterministic optimization.

The results of the optimization are tabulated in Table 2 and Figure 6.

## e-book Probabilistic Methods in Structural Engineering

A comparison of deterministic and probabilistic optimization of plate submitted to dynamic load indicates the reliability of both types of optimization. If there is consistency in the definition of the deterministic and the probabilistic load, the results of both types of optimization agree quite well.

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A better design in relation to the initial design is obtained in all the analyzed cases. In Example 1, with 4 design variables, the variable least altered is variable 1 h. This is to be expected as the elements near the point of application of the load must be more rigid. This example is illustrative, as the real plate has a constant thickness. Although the design variables are different in the two types of optimization, the values of the objective functions are quite similar for the cases with 2 and 4 design variables.

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This conclusion is to be expected as the two problems work with different design spaces and two different analyses, one deterministic and the other, probabilistic. Optimun design of plates structures under random loadings.

Rio de Janeiro, Brazil, Full tex in CD Rom. Tese de Doutorado. GOTO, S. Um elemento triangular para placas e cascas laminadas. Advances in structural optimization. Kluver Academic Publishers, SZE, K. Quadratic triangular Co plate bending element. International Journal of Numerical Methods in Engineering, v.

This is an Open Access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Services on Demand Journal. Civil Engineering Optimization of structures subjected to dynamic load: deterministic and probabilistic methods.

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Abstract This paper deals with the deterministic and probabilistic optimization of structures against bending when submitted to dynamic loads. Introduction A deterministic dynamic load is one whose value is determined in any instant and, consequently, the response value is determined in that instant by a deterministic analysis.

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The finite element model For the structural modeling of the plate, a 6-node triangular AST6 is used, and for the other examples, the beam element is used. Deterministic optimization According to Falco , the deterministic optimization problem consists in the minimization of the structural mass subjected to a condition whereby the displacement in a given point and in a given instant of time is equal or less than a given threshold.

This problem is formulated as follows: 1. Probabilistic optimization The equivalent probabilistic optimization problem is the minimization of the structural mass with the restriction that the probability of the displacement in a given point be greater than a given value that must be less than a given probability. The solution of the optimization problem The solution of the optimization problem presented through Equations 1 and 5 is performed by the Interior Points Method, Herskovits Consider the minimization problem: Examples The application example is the optimization of the isotropic plate depicted in Figure 1.

Design Variables Initial Final 1 D. Function kg Conclusion A comparison of deterministic and probabilistic optimization of plate submitted to dynamic load indicates the reliability of both types of optimization. This example is illustrative, as the real plate has a constant thickness Although the design variables are different in the two types of optimization, the values of the objective functions are quite similar for the cases with 2 and 4 design variables.

Received: September 14, ; Accepted: April 25,