Ren-Jye Yang

Stress-based topology optimization

Previous research on topology optimization focussed primarily on global structural behaviour such as stiffness and frequencies. However, to obtain a true optimum design of a vehicle structure, stresses must be considered. The major difficulties in stress based topology optimization problems are two-fold. First, a large number of constraints must be considered, since unlike stiffness, stress is a local quantity. This problem increases the computational complexity of both the optimization and sensitivity analysis associated with the conventional topology optimization problem. The other difficulty is that since stress is highly nonlinear with respect to design variables, the move limit is essential for convergence in the optimization process. In this research, global stress functions are used to approximate local stresses. The density method is employed for solving the topology optimization problems. Three numerical examples are used for this investigation. The results show that a minimum stress design can be achieved and that a maximum stiffness design is not necessarily equivalent to a minimum stress design.

Automotive applications of topology optimization

Topology optimization is used for obtaining the best layout of vehicle structural components to achieve predetermined performance goals. An in-house topology optimization software, TOP, has been developed to analyse important automotive components. The topology design problem is formulated as a general optimization problem and is solved by the mathematical programming method. The MSC/NASTRAN finite element code is employed for response analyses. The use of MSC/NASTRAN is significant, because it not only allows engineers to use a wellaccepted and widely-used finite element code with no size limit on the model, but also permits developers to concentrate on the rest of the topology optimization program. Three automotive examples including a simplified truck frame, a deck lid, and a space frame structure are presented.

Bead pattern optimization

Plane sheet panels exhibit poor stiffness and NVH (noise, vibration, and harshness) performance due to their flexibility. A common and cost-effective approach in the automotive industry to improve the stiffness and NVH peformance of sheet panels is the addition of beads. However, no systematic methodology is available for determining the optimal pattern of beads in sheet metal. This research explores the feasibility of applying topology optimization methods to the bead design of sheet panels. The approach starts with adding beam elements to the shell element model of the sheet panel to simulate the stiffness improvement of the structure and then uses the topology optimization method to obtain the optimal layout of the beam elements. A cantilever plate is used to perform a preliminary study for bead pattern design and a simplified vehicle structure is used to demonstrate the applicability of the proposed method.

Optimal fastener pattern design considering bearing loads

In many engineering structures, failure occurs either at the connection itself or in the component at the point of attachment of the connection. To extend the service life of the structure it is important to ensure that the loads borne by the connections are distributed as uniformly as possible. This would also minimize the possibility of localized high stress regions within the component. In this work a topology optimization based approach has been developed to incorporate fastener load constraints into a problem formulated for optimal location of fasteners. The computational results indicate that it is effective in reducing the maximum fastener loads without compromising on the overall stiffness of the structure.

Application of basis function concept to practical shape optimization problems

Component shape optimization normally requires a parameterized geometric representation or a generic model for the solid geometry which evolves to an optimal design. Generic models for large-scale three-dimensional components are difficult to build. The difficulties result from the lack of robust automatic mesh generation and the availability of a parametric model. To remedy this problem, a basis function concept used in mathematics for representing an arbitrary function is employed for geometric representation of solids. This approach does not require automatic mesh generation or parametric models for geometric representation and thus is suitable for large-scale complicated components. Numerical examples are used to demonstrate the applicability of this approach to realistic problems.

An excel based robust design tool for vehicle structural optimization

To reduce the cost of prototype and physical test, CAE analysis has been widely used to evaluate the vehicle performance during product development process. Combining CAE analysis and optimization approach, vehicle design process can be implemented more efficiently with affordable cost. Reliability based design optimization (RBDO) formulation considers variations of input variables, such as component gauges and material properties. As a result, the design obtained by using RBDO is more reliable and robust compared to those by deterministic optimization. The RBDO process starts from running simulation at DOE sampling data points, generating surrogate models (response surface) and performing robust and reliability based design optimization on the surrogate models by using Monte Carlo simulation. This paper presents a RBDO framework in Excel enviroment. Within this framework, the engineer can perform DOE sampling, surrogate modeling, robustness assessment, Monte Carlo simulation, robust design and reliability-based optimization with any type of distribution.

A Copula-Based Approach for Model Bias Characterization

Available methodologies for model bias identification are mainly regression-based approaches, such as Gaussian process, Bayesian inference-based models and so on. Accuracy and efficiency of these methodologies may degrade for characterizing the model bias when more system inputs are considered in the prediction model due to the curse of dimensionality for regression-based approaches. This paper proposes a copula-based approach for model bias identification without suffering the curse of dimensionality. The main idea is to build general statistical relationships between the model bias and the model prediction including all system inputs using copulas so that possible model bias distributions can be effectively identified at any new design configurations of the system. Two engineering case studies whose dimensionalities range from medium to high will be employed to demonstrate the effectiveness of the copula-based approach.

Bayesian Based Multivariate Model Validation Method Under Uncertainty for Dynamic Systems

Validation of computational models with multiple, repeated, and correlated functional responses for a dynamic system requires the consideration of uncertainty quantification and propagation, multivariate data correlation, and objective robust metrics. This paper presents a new method of model validation under uncertainty to address these critical issues. Three key technologies of this new method are uncertainty quantification and propagation using statistical data analysis, probabilistic principal component analysis (PPCA), and interval-based Bayesian hypothesis testing. Statistical data analysis is used to quantify the variabilities of the repeated tests and computer-aided engineering (CAE) model results. The differences between the mean values of test and CAE data are extracted as validation features, and the PPCA is employed to handle multivariate correlation and to reduce the dimension of the multivariate difference curves. The variabilities of the repeated test and CAE data are propagated through the data transformation to the PPCA space. In addition, physics-based thresholds are defined and transformed to the PPCA space. Finally, interval-based Bayesian hypothesis testing is conducted on the reduced difference data to assess the model validity under uncertainty. A real-world dynamic system example which has one set of the repeated test data and two stochastic CAE models is used to demonstrate this new approach.

CAE Model Validation in Vehicle Safety Design

This paperfocuses on the development of a framework of nonlinear finite element model validation for vehicle crash simulation. Integrated computational and test-based methods were discussed for validating computational models under physical, informational and model uncertaintes. Several methods were investigated to quantify transient time-domain data (functional data). The concept of correlation index was proposed to determine the degree to which a model is an accurate representation of the real world from the perspective of the intended uses of the model. The methodologies developed in this paper can also be used for CAE model updating, parameter tuning, and model calibration.

Shape optimal design of an engine exhaust manifold

An engine exhaust manifold made of cast iron cracks during thermal shock testing. The test process is simulated by finite element analysis. The manifold is formulated as a linear heat transfer and thermoelasticity problem in a variational form. Analytical expressions for shape design sensitivities of general three-dimensional problems are presented, using the material derivative approach. A hybrid approach is described and used during the optimization process. This approach takes advantage of the direct and the adjoint variable methods and is the most efficient in calculating the sensitivity of the structural responses. After the finite element model is verified by comparing the results with those from testing, the engine exhaust manifold is optimized with respect to its geometry.