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The Energy Finite Element Analysis (EFEA) has been developed for computing the structural vibration and the interior noise level of complex structural-acoustic systems by solving numerically governing differential equations with energy densities as primary variables. In this paper a complete simulation process for evaluating airborne noise in an automotive vehicle is presented and validated through extensive comparison to test data. The theoretical elements associated with the important paths of the noise transfer from the exterior of the vehicle to the interior acoustic space are discussed. The steps required for developing an EFEA model for a vehicle are presented. The model is developed based on the physical construction of the vehicle system and no test measurements are utilized for adjusting the numerical model.

The Energy Finite Element Analysis(EFEA) is a recent development for high frequency vibro-acoustic analysis, and constitutes an evolution in the area of high frequency computations. The EFEA is a wave based approach, while the SEA is a modal based approach. In this paper the similarities in the theoretical development of the two methods are outlined. The main scope of this paper is to establish the validity of the EFEA by analyzing several complex structural-acoustic systems. The EFEA solutions are compared successfully to SEA results and to solutions obtained from extremely dense conventional FEA models.

This paper presents a validation case study for an Energy Finite Element Analysis (EFEA) formulation through comparison to test data. The EFEA comprises a simulation tool for computing the structural response of a complex structure and the amount of the radiated power. The EFEA formulation presented in this paper can account for periodic stiffeners, for partial fluid loading effects on the outer part of the structure, and for internal compartments filled with heavy fluid. In order to validate these modeling capabilities of the EFEA two 1/8th scale structures representing an advanced double hull design and a conventional hull design of a surface ship are analyzed. Results for the structural vibration induced on the outer bottom part of the structure are compared to available test data. The excitation is applied at two different locations of the deck structure. Good correlation is observed between the numerical results and the test data.

The hybrid Finite Element Analysis (hybrid FEA) has been developed for performing structure-borne computations in automotive vehicle structures [1, 2 and 3]. The hybrid FEA method combines conventional FEA with Energy FEA (EFEA). Conventional FEA models are employed for modeling the behavior of the stiff members in a system. Appropriate damping and spring or mass elements are introduced in the connections between stiff and flexible members in order to capture the presence of the flexible members during the analyses of the stiff ones. The component mode synthesis method is combined with analytical solutions for determining the driving point conductance at joints between stiff and flexible members and for defining the properties of the concentrated elements which represent the flexible members when analyzing the stiff components.

A multi-disciplinary optimization analysis is a highly iterative process that requires a large number of function evaluations for computing the objective functions and the constraints. Metamodels (i.e. response surface methodologies) can be constructed before starting the optimization for each one of the objective functions and the constraint functions. The metamodels can be employed in the multi-discipline optimization instead of high fidelity simulations resulting in significant computational savings. A multi-discipline design optimization of an aircraft wing under aerodynamic and structural analysis considerations is performed in this manner. Design variables associated with the shape of the wing are considered in the CFD simulations, while sizing structural design variables are considered in the structural discipline. At the top system level, a cost type metric is defined for driving the overall design optimization process.

In this paper the development of statistical metamodels and statistical fast running models is presented first. They are utilized for propagating uncertainties in a multi-discipline design optimization process. Two main types of uncertainty can be considered in this manner: uncertainty due to variability in design variables or in random parameters; uncertainty due to the utilization of metamodels instead of the actual simulation models during the optimization process. The value of the new developments and their engagement in multi-discipline design optimization is demonstrated through a case study. An underwater vehicle is designed under four different disciplines, namely, noise radiation, self-noise due to TBL excitation, dynamic response due to propulsion impact loads, and response to an underwater detonation.

The hybrid FEA method combines the conventional FEA method with the energy FEA (EFEA) for computing the structural vibration in vehicle structures when the excitation is applied on the load bearing stiff structural members. Conventional FEA models are employed for modeling the behavior of the stiff members in the vehicle. In order to account for the effect of the flexible members in the FEA analysis, appropriate damping and spring/mass elements are introduced at the connections between stiff and flexible members. Computing properly the values of these damping and spring/mass elements is important for the overall accuracy of the computations. Utilizing in these computations the analytical solutions for the driving point impedance of infinite or semi-infinite members introduces significant approximations.

The Energy Finite Element Analysis (EFEA) has been validated in the past through comparison with test data for computing the structural vibration and the radiated noise for Naval systems in the mid to high frequency range. A main benefit of the method is that it enables fast computations for full scale models. This capability is exploited by using the EFEA for a submarine pressure hull design optimization study. A generic but representative pressure hull is considered. Design variables associated with the dimensions of the king frames, the thickness of the pressure hull in the vicinity of the excitation (the latter is considered to be applied on the king frames of the machinery room), the dimensions of the frames, and the damping applied on the hull are adjusted during the optimization process in order to minimize the radiated noise in the frequency range from 1,000Hz to 16,000Hz.

In the Energy Finite element Analysis (EFEA) method, the governing differential equations are formulated for an energy variable that has been spatially averaged over a wavelength and time averaged over a period. A finite element approach is used for solving the differential equations numerically. Therefore, a library of elements is necessary for modeling the various wave bearing domains that are present in a structural-acoustic system. Discontinuities between wave bearing domains always exist due to the geometry, from a change in material properties, from multiple components being connected together, or from different media interfacing with each other. Therefore, a library of joints is also necessary for modeling the various types of physical connections which can be encountered in a structural-acoustic system.

A comprehensive formulation is presented for the dynamics of a rotating flexible crankshaft coupled with the dynamics of an engine block through a finite difference elastohydrodynamic main bearing lubrication algorithm. The coupling is based on detailed equilibrium conditions at the bearings. The component mode synthesis is employed for modeling the crankshaft and block dynamic behavior. A specialized algorithm for coupling the rigid and flexible body dynamics of the crankshaft within the framework of the component mode synthesis has been developed. A finite difference lubrication algorithm is used for computing the oil film elastohydrodynamic characteristics. A computationally accurate and efficient mapping algorithm has been developed for transferring information between a high - density computational grid for the elastohydrodynamic bearing solver and a low - density structural grid utilized in computing the crankshaft and block structural dynamic response.

High-Reynolds number turbulent boundary layers are an important source for inducing structural vibration. Small geometric features of a structure can generate significant turbulence that result in structural vibration. In this work we develop a new method to couple a high-fidelity fluid solver with a dynamic hybrid analytical-numerical formulation for the structure. The fluid solver uses the Large-Eddy Simulation closure for the unresolved turbulence. Specifically, a local and dynamic one-equation eddy viscosity model is employed. The fluid pressure fluctuation on the structure is mapped to the dynamic structural model. The plate where the flow excitation is applied is considered as part of a larger structure. A hybrid approach based on the Component Mode Synthesis (CMS) is used for developing the new hybrid formulation. The dynamic behavior of the plate which is excited by the flow is modeled using finite elements.

One of the main threats to military vehicles originates from landmine blasts. In order to improve the survivability of the occupants it is important to design a military vehicle for increased occupant safety. Simulation technology that combines modeling of the blast loads from the landmine explosion, the response of the vehicle to the blast load, and the loads developed on the members of an occupant are important factors in this effort. Uncertainties from the soil properties can influence the blast loads and thus the occupants' safety. In this paper, principal component analysis along with metamodel theory are employed for developing fast running models for the response functions of interest. The response functions of interest are the time domain loads which are developed on an occupant's members due to the blast. The fast running models allow assessing the probability level associated with injury for an occupant.

Utilizing simulation technology is important for designing a structure with increased survivability to a load from an explosion. The pressure wave from the blast and the fragments hitting the structure must be simulated in such an analysis. Commercial software can be utilized through the development of appropriate interfaces for performing such computations. In this paper an approach is presented for combining commercially available Eulerian and Lagrangian solvers for performing blast event simulations. A capability has been developed for automatically creating the Eulerian finite element given the finite element model for the structure. The effect of moisture in the soil properties is considered during the generation of the soil - explosive - air model used by the Eulerian solver. Tracers are defined in the Eulerian model for all structural finite elements which are on the outer part of the structure and are subjected to the load from the blast.

This paper presents the development of surrogate models (metamodels) for evaluating the bearing performance in an internal combustion engine. The metamodels are employed for performing probabilistic analyses for the engine bearings. The metamodels are developed based on results from a simulation solver computed at a limited number of sample points, which sample the design space. An integrated system-level engine simulation model, consisting of a flexible crankshaft dynamics model and a flexible engine block model connected by a detailed hydrodynamic lubrication model, is employed in this paper for generating information necessary to construct the metamodels. An optimal symmetric latin hypercube algorithm is utilized for identifying the sampling points based on the number and the range of the variables that are considered to vary in the design space.

This paper presents the development of surrogate models (metamodels) for evaluating the bearing performance in an internal combustion engine without performing time consuming analyses. The metamodels are developed based on results from actual simulation solvers computed at a limited number of sample points, which sample the design space. A finite difference bearing solver is employed in this paper for generating information necessary to construct the metamodels. An optimal symmetric Latin hypercube algorithm is utilized for identifying the sampling points based on the number and the range of the variables that are considered to vary in the design space. The development of the metamodels is validated by comparing results from the metamodels with results from the actual bearing performance solver over a large number of evaluation points. Once the metamodels are established they are employed for performing probabilistic analyses.

A fast and accurate journal bearing elastohydrodynamic analysis is presented based on a finite difference formulation. The governing equations for the oil film pressure, stiffness and damping are solved using a finite difference approach. The oil film domain is discretized using a rectangular two-dimensional finite difference mesh. In this new formulation, it is not necessary to generate a global fluidity matrix similar to a finite element based solution. The finite difference equations are solved using a successive over relaxation (SOR) algorithm. The concept of “Influence Zone,” for computing the dynamic characteristics is introduced. The SOR algorithm and the “Influence Zone” concept significantly improve the computational efficiency without loss of accuracy. The new algorithms are validated with numerical results from the literature and their numerical efficiency is demonstrated.

In this paper a Multi-Level System (MLS) optimization algorithm is presented and utilized for the multi-discipline design of a ground vehicle track. The MLS can guide the decision making process for designing a complex system where many alternatives and many mutually competing objectives and disciplines need to be considered and evaluated. Mathematical relationships between the design variables and the multiple discipline performance objectives are developed adaptively as the various design considerations are evaluated and as the design is being evolved. These relationships are employed for rewarding performance improvement during the decision making process by allocating more resources to the disciplines which exhibit the higher level of improvement. The track analysis demonstrates how a multi-discipline design approach can be pursued in ground vehicle applications.

Stiffened panels are encountered in many engineering systems since the stiffeners comprise the mechanism which provides support and rigidity to the panel's skin. Either a mechanical excitation or an acoustic load can be applied on a stiffened panel creating vibration that is transmitted in all panel components. Mechanical excitation tends to be localized in nature, originating from operating machinery mounted on the panel, while the acoustic excitation tends to be distributed over the entire panel, since it typically originates from an external acoustic source which creates an acoustic field impinging on the entire panel. In the Energy Finite Element Analysis (EFEA) various degrees of fidelity are possible when modeling the response of a stiffened panel. In this paper, the theoretical background and the corresponding implications associated with each alternative modeling approach are presented first.

In order to develop confidence in numerical models which are used for automotive crash simulations, results are compared with test data. Modeling assumptions are made when constructing a simulation model for a complex system, such as a vehicle. Through a thorough understanding of the modeling assumptions an appropriate set of variables can be selected and adjusted in order to improve correlation with test data. Such a process can lead to better modeling practices when constructing a simulation model. Comparisons between the time history of acceleration responses from test and simulations are the most challenging. Computing accelerations correctly is more difficult compared to computing displacements, velocities, or intrusion levels due to the second order differentiation with time. In this paper a methodology for enabling the update of a simulation model for improved correlation is presented.

Numerical models are used for computing the shock response in many areas of engineering applications. Current analysis methods do not account for uncertainties in the model parameters. In addition, when numerical models are calibrated based on test data neither the uncertainty which is present in the test data nor the uncertainty in the model are taken into account. In this paper an approach for model update under uncertainty and error estimation for shock applications is presented. Fast running models are developed for the model update based on principal component analysis and surrogate models. Once the numerical model has been updated the fast running models are employed for performing probabilistic analyses and estimate the error in the numerical solution. The new developments are applied for computing the shock response of large scale structures, updating the numerical model based on test data, and estimating the error in the predictions.