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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.

A special spot weld element (SWE) is presented for simplified representation of spot joints in complex structures for structural durability evaluation using the mesh-insensitive structural stress method. The SWE is formulated using rigorous linear four-node Mindlin shell elements with consideration of weld region kinematic constraints and force/moments equilibrium conditions. The SWEs are capable of capturing all major deformation modes around weld region such that rather coarse finite element mesh can be used in durability modeling of complex vehicle structures without losing any accuracy. With the SWEs, all relevant traction structural stress components around a spot weld nugget can be fully captured in a mesh-insensitive manner for evaluation of multiaxial fatigue failure.

In applications of the Energy Finite Element Analysis (EFEA) there is an increasing need for developing comprehensive models with a large number of elements which include both structural and interior fluid elements, while certain parts of the structure are considered to be exposed to an external fluid loading. In order to accommodate efficient computations when using simulation models with a large number of elements, joints, and domains, a substructuring computational capability has been developed. The new algorithm is based on dividing the EFEA model into substructures with internal and interface degrees of freedom. The system of equations for each substructure is assembled and solved separately and the information is condensed to the interface degrees of freedom. The condensed systems of equations from each substructure are assembled in a reduced global system of equations. Once the global system of equations has been solved the solution for each substructure is pursued.

This paper presents a comprehensive damage model capable of predicting crash behavior of aluminum structures under varying applied loading conditions. The damage model has been implemented in a general purpose explicit nonlinear finite element code and crash analysis has been carried out for aluminum tubes. The response obtained from the finite element analysis shows a close agreement with the experimental data. The finite element program containing the proposed generalized damage model can be used to analyze aluminum structures subjected to complex service loading conditions and identify associated failure modes to assess crashworthiness.

The paper presents a method of analysis based on the theory of damage mechanics to quantify the degree of damage in an engineering structure under load. The method is incorporated into a Ford in-house finite element program called FCRASH that is applied to analyze the cumulative damage in a bumper under multiple low speed impacts. The numerical results calculated at the peak value of the contact force are compared with the test results. The FEA results are used to identify the locations of the hotspot in the bumper system and the predicted location where a potential crack would initiate. The microscopic observations showed damage in the area predicted with the finite element program after the specified number of impacts.

In FOA (First Order Analysis) any vehicle body structure might be interpreted as a collective simple structure that can be decomposed into 3 fundamental structure types. The first structure is the “BEAM”, whose cross sectional properties as well as its material dominates the mechanical behavior, the second is the “PANEL (shear panel, plate, and shell)”, whose mechanical behavior can be varied by changing its geometrical properties in the thickness direction, i.e. adding beads or flanges. The third structure is the “JOINT”, which connects the proceeding structures, and transfer complex three-dimensional loads with three-dimensional deformation. In the present work, we shall propose a methodology to identify a portion of an arbitrary FE model of an automotive body structure, with a “BEAM” structure in the FOA approach. In the latter chapter of this paper, cross section loads will be related with cross sectional properties in the aspect of the element strain energy concept.

Tubular sections are found in many automotive structural components such as front rails, cross beams, and sub-frames. They are also used in other vehicular structures, such as buses and rails. In many of these components, smaller tubular sections may be joined together using an adhesive to build the required structure. For crash safety applications, it is important that the joined tube sections be able to provide high energy absorption capability and withstand the impact load before the adhesive bond failure occurs. In this study, single lap tubular joints between two aluminum tubes are investigated for their crush performance at both quasi-static and high impact speeds using finite element analysis. A crash optimized adhesive Betamate 1496 is considered. The joint parameters, such as adhesive overlap length, tube diameters and tube lengths, are varied to determine their effects on energy absorption, peak and mean loads, and tube deformation mode.

Closed-form structural stress solutions are investigated for fatigue life estimations of flow drill screw (FDS) joints in lap-shear specimens of aluminum 6082-T6 sheets with and without clearance hole based on three-dimensional finite element analyses. The closed-form structural stress solutions for rigid inclusions under counter bending, central bending, in-plane shear and in-plane tension are first presented. Three-dimensional finite element analyses of the lap-shear specimens with FDS joints without and with gap (with and without clearance hole) are then presented. The results of the finite element analyses indicate that the closed-form structural stress solutions are quite accurate at the critical locations near the FDS joints in lap-shear specimens without and with gap (with and without clearance hole) for fatigue life predictions.

A new closed-form structural stress solution for a spot weld in a square thin plate under central bending conditions is derived based on the thin plate theory. The spot weld is treated as a rigid inclusion and the plate is treated as a thin plate. The boundary conditions follow those of the published solution for a rigid inclusion in a square plate under counter bending conditions. The new closed-form solution indicates that structural stress solution near the rigid inclusion on the surface of the plate along the symmetry plane is larger than those for a rigid inclusion in an infinite plate and a finite circular plate with pinned and clamped outer boundaries under central bending conditions. When the radius distance becomes large and approaches to the outer boundary, the new analytical stress solution approaches to the reference stress whereas the other analytical solutions do not.

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.

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.

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.

In frontal collision of vehicles, the front bumper system is the first structural member that receives the energy of collision. In low speed impacts, the bumper beam and the crush cans that support the bumper beam are designed to protect the engine and the radiator from being damaged, while at high speed impacts, they are required to transfer the energy of impact as uniformly as possible to the front rails that contributes to the occupant protection. The bumper beam material today is mostly steels and aluminum alloys, but carbon fiber composites have the potential to reduce the bumper weight significantly. In this study, crash performance of bumper beams made of a boron steel, aluminum alloy 5182 and a carbon fiber composite with steel crush cans is examined for their maximum deflection, load transfer to crush cans, total energy absorption and failure modes using finite element analysis.

This paper presents an extension of our previous work on decomposition-based assembly synthesis [1], where the 3D finite element model of a vehicle body-in-white (BIW) is optimally decomposed into a set of components considering the stiffness of the assembled structure under given loading conditions, and the manufacturability and assemblability of each component. The stiffness of the assembled structure is evaluated by finite element analyses, where spot-welded joints are modeled as linear torsional springs. In order to allow close examinations of the trade-off among stiffness, manufacturability, and assemblability, the optimal decomposition problem is solved by multi-objective genetic algorithm [2,3], with graph-based crossover [4,5], combined with FEM analyses, generating Pareto optimal solutions. Two software programs are developed to implement the proposed method.

This study presents an efficient process to optimize the transmission loss of a vehicle muffler by using both experimental and analytical methods. Two production mufflers were selected for this study. Both mufflers have complex partitions and one of them was filled with absorbent fiberglass. CAD files of the mufflers were established for developing FEA models in ANSYS and another commercial software program (CFEA). FEA models were validated by experimental measurements using a two-source method. After the models were verified, sensitivity studies of design parameters were performed to optimize the transmission loss (TL) of both mufflers. The sensitivity study includes the perforated hole variations, partition variations and absorbent material insertion. The experimental and sensitivity analysis results are included in the paper.

In this paper, an analytical method is proposed for determining the stress distributions in steering knuckle/tapered stud assemblies. The method is based on solutions of the plane stress thick cylinder interference fit problem with modifications to account for the effects of stud taper and dissimilar component materials. The analytical solutions are applied to knuckle/tapered stud assemblies. The results from the analytical solutions are compared to those from a finite element analysis. It is shown that the analytical and FEA results are in good agreement for several load and frictional conditions, and the hoop and radial stress solutions presented in this paper are good engineering solutions to the knuckle/tapered stud problem where the draw distance is provided.

The shape and topology optimization method using a homogenization method is a powerful design tool because it can treat topological changes of a design domain. This method was originally developed in 1988 [1] and have been studied by many researchers. However, their scope of application in real vehicle design works has been limited where a design domain and boundary conditions are very complicated. The authors have developed a powerful optimization system by adopting a general purpose finite element analysis code. A method for treating vibration problems is also discussed. A new objective function corresponding to a multi-eigenvalue optimization problem is suggested. An improved optimization algorithm is then applied to solve the problem. Applications of the optimization system to design the body and the parts of a solar car are presented.

This study considers the thermal stresses in single lap adhesive joints between magnesium and steel. The source of thermal stresses is the large difference in the coefficients of thermal expansion of magnesium and steel. Two different temperature differentials from the ambient conditions (23°C) were considered, namely -30°C and +50°C. Thermal stresses were determined using finite element analysis. In addition to Mg-steel substrate combination, Mg-Mg and steel-steel combinations were also studied. Combined effect of temperature variation and applied load was also explored. It was observed that temperature increase or decrease can cause significant thermal stresses in the adhesive layer and thermal stress distribution in the adhesive layer depends on the substrate combination and the applied load.

In this paper, the evolution equation for the active yield surface during the unloading/reloading process based on the pressure-sensitive Drucker-Prager yield function and a recently developed anisotropic hardening rule with a non-associated flow rule is first presented. A user material subroutine based on the anisotropic hardening rule and the constitutive relation was written and implemented into the commercial finite element program ABAQUS. A two-dimensional plane strain finite element analysis of a crankshaft section under fillet rolling was conducted. After the release of the roller, the magnitude of the compressive residual hoop stress for the material with consideration of pressure sensitivity typically for cast irons is smaller than that without consideration of pressure sensitivity. In addition, the magnitude of the compressive residual hoop stress for the pressure-sensitive material with the non-associated flow rule is smaller than that with the associated flow rule.

In this paper, a microstructure-based three-dimensional (3D) finite element modeling method is adopted to investigate the effects of porosity in thin-walled high pressure die-cast (HPDC) magnesium alloys on their ductility. For this purpose, the cross-sections of AM60 casting samples are first examined using optical microscope and X-ray tomography to obtain the general information on the pore distribution features. The experimentally observed pore distribution features are then used to generate a series of synthetic microstructure-based 3D finite element models with different pore volume fractions and pore distribution features. Shear and ductile damage models are adopted in the finite element analyses to induce the fracture by element removal, leading to the prediction of ductility.