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The Hybrid Finite Element Analysis (HFEA) method is based on combining conventional Finite Element Analysis (FEA) with analytical solutions and energy methods for mid-frequency computations. The method is appropriate for computing the vibration of structures which are comprised by stiff load bearing components and flexible panels attached to them; and for considering structure-borne loadings with the excitations applied on the load bearing members. In such situations, the difficulty in using conventional FEA at higher frequencies originates from requiring a very large number of elements in order to capture the flexible wavelength of the panel members which are present in a structure. In the HFEA the conventional FEA model is modified by de-activating the bending behavior of the flexible panels in the FEA computations and introducing instead a large number of dynamic impedance elements for representing the omitted bending behavior of the panels.

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.

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.

Assessing the dynamic performance of multilayer plates subjected to impulsive loading is of interest for identifying configurations that either absorb energy or transmit the energy in the transverse directions, thereby mitigating the through-thickness energy propagation. A reduced-order modeling approach is presented in this paper for rapidly evaluating the structural dynamic performance of various multilayer plate designs. The new approach is based on the reverberation matrix method (RMM) with the theory of generalized rays for fast analysis of the structural dynamic characteristics of multilayer plates. In the RMM model, the waves radiated from the dynamic load are reflected and refracted at each interface between layers, and the waves within each layer are transmitted with a phase lag. These two phenomena are represented by the global scattering matrix and the global phase matrix, respectively.

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.

The Hybrid FEA method is based on combining conventional Finite Element Analysis (FEA) with Energy Finite Element Analysis (EFEA) for mid-frequency computations. The difficulty in using conventional FEA at higher frequencies originates from requiring a very large number of elements in order to capture the flexible wavelength of the panel members which are present in a structure. In the Hybrid FEA the conventional FEA model is modified by de-activating the bending behavior of the flexible panels in the FEA computations and introducing instead a large number of dynamic impedance elements for representing the omitted bending behavior. The excitation is considered to be applied on the conventional FEA model and the vibration analysis is conducted. The power flow through the dynamic impedance elements is computed and applied as excitation to the EFEA model of the flexible panels. The EFEA analysis computes the vibration of the flexible panels.

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.

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.

The Energy Finite Element Analysis (EFEA) has been utilized successfully for modeling complex structural-acoustic systems with isotropic structural material properties. In this paper, a formulation for modeling structures made out of composite materials is presented. An approach based on spectral finite element analysis is utilized first for developing the equivalent material properties for the composite material. These equivalent properties are employed in the EFEA governing differential equations for representing the composite materials and deriving the element level matrices. The power transmission characteristics at connections between members made out of non-isotropic composite material are considered for deriving suitable power transmission coefficients at junctions of interconnected members. These coefficients are utilized for computing the joint matrix that is needed to assemble the global system of EFEA equations.

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.

Vehicle design is a complex process requiring interactions and exchange of information among multiple disciplines such as fatigue, strength, noise, safety, etc. Simulation models are employed for assessing and potentially improving a vehicle's performance in individual technical areas. Challenges arise when designing a vehicle for improving mutually competing objectives, satisfying constraints from multiple engineering disciplines, and determining a single set of values for the vehicle's characteristics. It is of interest to engage simulation models from the various engineering disciplines in an organized and coordinated manner for determining a design configuration that provides the best possible performance in all disciplines. The multi-discipline design process becomes streamlined when the simulation methods integrate well with finite element or computer aided design models.

In order to be effective and maximize the weight and cost savings when designing for noise and vibration attributes, the structural-acoustics design effort must be concurrent with the efforts of other engineering disciplines (i.e. durability, crashworthiness, etc.). In this manner, it will be possible to account for the effects of structural changes across disciplines and improve the NVH performance while the structure is being configured rather than attempting to improve NVH characteristics after the structural design has been completed.

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 developed for evaluating the vibro-acoustic behavior of complex systems. In the past EFEA results have been compared successfully to measured data for Naval, automotive, and aircraft systems. The main objective of this paper is to present information about the process of developing EFEA models for two configurations of a business jet, performing analysis for computing the vibration and the interior noise induced from exterior turbulent boundary layer excitation, and discussing the correlation between test data and simulation results. The structural EFEA model is generated from an existing finite element model used for stress analysis during the aircraft design process. Structural elements used in the finite element model for representing the complete complex aircraft structure become part of the EFEA structural model.

A multi-disciplinary optimization under uncertainty (MDO-U) capability has been developed in order to solve optimization problems with multiple sets of objectives and constraints originating from different design disciplines while simultaneously accounting for uncertainty during the optimization process. Uncertainties are introduced in the optimization process by considering the constraints which depend on any random variables and any random parameters as probabilistic. Satisfying the probabilistic constraints in the presence of uncertainty introduces sufficient conservatism in the solution and eliminates the need for further application of safety factors. The MDO-U capability is applied for performing design optimization for the TPS of an Apollo type vehicle. The Traj and FIAT codes of NASA Ames are employed during this design process for trajectory and for thermal analyses, respectively.

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 Energy Boundary Element Analysis (EBEA) has been utilized in the past for computing the exterior acoustic field at high frequencies (above ∼400Hz) around vehicle structures and numerical results have been compared successfully to test data [1, 2 and 3]. The Energy Finite Element Analysis (EFEA) has been developed for computing the structural vibration of complex structures at high frequencies and validations have been presented in previous publications [4, 5]. In this paper the EBEA is utilized for computing the acoustic field around a vehicle structure due to external acoustic noise sources. The computed exterior acoustic field comprises the excitation for the EFEA analysis. Appropriate loading functions have been developed for representing the exterior acoustic loading in the EFEA simulations, and a formulation has been developed for considering the acoustic treatment applied on the interior side of structural panels.

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 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.