**5. Conclusion**

This chapter has proposed risk performance indexes to improve the efficiency of the general performance measurement for mega projects by extending the existing cost/schedule-based performance measurement system. The expected effects of the risk performance index method proposed in this study can be summarized as follows.

**12** 

*Latvia* 

**Shape Optimization of Mechanical** 

Alexander Janushevskis, Janis Auzins,

*Riga Technical University,* 

Anatoly Melnikovs and Anita Gerina-Ancane

 **Components for Measurement Systems** 

For the topology and shape optimization of structures, the different realizations of homogenization method are widely used (Arora, 2004; Bendsoe & Sigmund, 2003). This method is highly effective for shell constructions and allows implementing topometry and topography, sizing and shape as well as freeform optimization (Vanderplaats, 2004). However, it is a very time consuming procedure because the number of design parameters can reach a million and more. There is the possibility of taking into account some technological factors, nevertheless, in the case of bulky bodies it frequently produces shapes that are difficult to manufacture. As shown in work (Mullerschon et al., 2010), the Hybrid Cellular Automata method does not allow parallelization of computations and PBS queuing system has been used. At the same time the following resource saving approach (Janushevskis et al., 2010; Janushevskis & Melnikovs, 2010) can be used for shape optimization which includes the following steps: 1) Planning the position of control points of NURBS (see, for example, Saxena & Sahay, 2005) for obtaining a smooth shape. 2) Building geometrical models using CAD software in conformity with design of experiment. 3) Calculation of responses for a complete FEM model using CAE software. 4) Building metamodels (surrogate models) for responses on the basis of computer experiment. 5) Using metamodels for shape optimization. 6) Validating the optimal design using CAE software

Latin Hypercube type experimental designs first proposed by Vilnis Eglajs in his work (Audze & Eglajs, 1977), then by McKay (McKay et al., 1979) and used by many other investigators, as well as its improvements (Auzins, 2004) are a very essential aspect utilized in the proposed method. The significance of approximations for the solution of optimization problems proposed by Lucien Schmit in his early works (Schmit & Farcshi, 1971) and nowadays generally recognized as the Response Surface Method is also the foundation of current approach. The use of planned computer experiments and the metamodeling (surrogate model) approach (Forrester et al., 2008; Sacks et al., 1989) ensures great economy of computing time, especially for finite element (FEM) calculations. First of all let us

**1. Introduction** 

for the complete FEM model.

demonstrate our approach on the simple test problems.

**2. Basics of approach** 

First, we constructed our system to be similar to the EVMS, which is the existing cost/schedule integrated performance measurement method. It is therefore possible to conduct three-dimensional integrated performance management using the 18 detailed indexes and variables employed in the risk performance index.

Second, we can perform integrated qualitative performance measurement for cost/schedule/risk by measuring the risk-related cost performance index and schedule performance index.

Third, we can perform integrated quantitative performance measurement for cost/schedule/risk by measuring the cost impact variance, the schedule impact variance, the cost risk response variance, and the schedule risk response variance.

Fourth, we can measure the risk response efficiency by comparing the cost impact variance with the actual response cost, and we have proposed a method to analyze the extra project expenses and actual response cost at a particular point during the project.

Furthermore, using the risk performance measurement of 'Low rate of apartment sales' as an example, the theoretical and practical value and validity of our risk performance indexes and measurement system can be summarized as follows: first, because risk is a dynamic phenomenon, the forecasting and reevaluation of risk factors should be performed periodically; second, our risk performance indexes provide the theoretical foundation for an integrated evaluation of cost and scheduling risks inherent in housing redevelopment projects; and third, by using our risk performance indexes and measurement model, a project team is required to forecast and evaluate project uncertainties and risks continually, thereby generating more proactive and diverse analyses than the traditional EVMS model.
