Multiple scale methods for the nonlinear analysis of a compressible fluid-structure interaction system are being developed. A Petrov-Galerkin function will be used as the weighting function for the compressible fluid dynamic equations due to the presence of the convective term. The response of a dynamic system will be decomposed into fast and slow time scales using temporal shifting.
This research deals with finite element methods for penetration mechanics: the development of a contact-impact algorithm which is easily vectorizable and can be implemented on partitioned memory SIMD computers, and the development of stable, one-point quadrature elements with hour glass control based on physical parame ters.
Multi-scale Petrov-Galerkin methods are being developed for the study of struc tural/building systems in which the response is characterized by multiple-spatial and multiple-time scales.
Experimental procedures and physical and mathematical models of the Chrysler hydromount are being developed to identify model parameters and evaluate mount performance. Physical design related to performance is also being investigated.
Multiple scale methods, which are based on reproducing kernel and wavelet analy sis, are developed. These permit the response of a system to be separated into different scales. These scales can either be the wave numbers corresponding to spatial variables or the frequencies corresponding to temporal variables; each scale response can be examined separately. This complete characterization of the unknown response is performed through the integral window transform; a space-scale and time-fre quency localization process is achieved by dilating the flexible multiple scale window function.
A generalized and unified constitutive law will be developed that describes the thermomechanical behavior of shape memory materials in terms of their martensitic phase transformations. This research will utilize mathematical and numerical methods and limited experimen tal testing, combined with detailed under standing of the micro mechanical material behavior. Novel aspects of the proposed work will address the history of transfor mation return points, multi-dimensional behavior, two-way memory effects and irreversible plasticity.
The proposed work is an effort to systematically examine the effects of physical and chemical aging on polymer composite materials with the goal of developing a model that can predict the long term response of these materials to general thermomechanical loading cycles. Data from creep characterization experi ments will be used to develop a nonlinear viscoelastic constitutive model which can include the coupled effects of aging and thermal history.
Methods of computational mechanics, including the finite element method (FEM) and the element-free Galerkin method (EFG) are applied to the study of nucleation and growth of phase transfor mations in solids. Landau-Ginzburg meth ods, together with FEM and EFG are used to study nucleation from classical to non-classical. The EFG method is used to deal with interface mobility in the growth of phase transformations. General aspects of gridless methods for problems in microme chanics and fracture are also being considered.
Environmental considerations and pending legislation threaten the use of lead base solders in several industries. Electronic and automotive industries, for example, are faced with finding lead-free solders with comparable or superior properties to the Pb-Sn solders currently in use. This project deals with the development of constitutive properties and fatigue lifetime prediction methodologies for candidate lead-free solders, such as Sn-Ag. It is important to recognize that typical operat ing temperatures for solders can be as much as fifty percent of the melting temperature and thus a variety of inelastic creep and deformation mechanisms must be accounted for.
Computational methodologies are being developed for quantitative prediction of probability of failure due to fatigue damage in aircraft components (such as at rivet holes in fuselage lap splices). Finite element, boundary element and element-free Galerkin methods are all being used in conjunction with first order reliability methods to perform risk assessments and to help set inspection schedules.
Probabilistic computational methods (finite element, boundary element and element-free Galerkin methods) are being applied to the study of fatigue reliability in automotive components. Used in conjunc tion with Monte Carlo, first order reliability or stochastic differential equation tech niques, these computational methods provide a powerful tool for determination of failure when failure probabilities are extremely low. The effects of pre-service and/or in-service inspections are incorpo rated into the analyses and special attention is given to warranty issues.
The finite element method is being used to study interface fracture mechanics in proposed high temperature, fiber-reinforced ceramic composite systems. Methods for the analysis of novel experiments are being developed. Fundamental investiga tions into the effects of a reaction product interlayer between the fiber and matrix are being carried out. The role of material anisotropy and also matrix creep are being explored with a view to understanding factors which affect interface fracture toughness.
We develop adaptive methods pseudo-spectral methods for the solution of problems exhibiting localized regions of rapid variation. In the method mappings are employed, so that in the mapped coordinate system the solutions vary gradually. The mappings are chosen dy namically so as to minimize functionals of the solution which measure the numerical error. In particular we study the role of imperfections and thermal coupling in the development of shear bands.
We employ adaptive pseudo-spectral methods to study the transition from laminar to turbulent combustion by deter mining increasingly complex modes of combustion. We identify the physical effects which promote the transition to more complex behavior and determine the role that different physical parameters have on the computed patterns. We study problems in both gaseous and condensed phase combustion.
We have acquired a Silicon Graphics Indigo 2 together with associated periph eral equipment to allow visualization of numerical computations in solid mechanics and combustion.
Computational methods are being used to study material failure processes such as shear bands and the growth of cracks. Emphasis is being placed on two types of methods: adaptive methods, in which the mesh is refined by subdivision of elements where needed, and element-free Galerkin methods.
Computational methods are being devel oped for the simulation of automobile crash. The work consist of three tasks:
Multiple scale methods, which are based on discrete and continuous reproducing kernels, wavelets, and integral window transforms will be developed for the analysis of complex structures with particular emphasis on compressible flow-structure systems. In this development, a microscope will be constructed with a flexible space-time localized window function which will translate and dilate in space and time to cover the entire domain of interest. The complete characterization of the unknown response is achieved by dilating the flexible multiple-scale window function. The zoom in and zoom out capability of the window function is especially useful in examining complex flow phenomena, such as flow induced vibration, dynamic stability of flow-structure interaction, turbulence structures, and high frequency structural dynamics response.
Multiple scale methods will be developed and applied to structural acoustic and structural dynamics with particular reference to fluid-structure interaction. These methods will provide the capability to make efficient and accurate computations of structural response which combine both the low and medium part of the spectrum. This new development will enable engineers not only to bring more detail into their structural system models, but will also enhance the computer simulations of many classes of multiple scale structural analysis. It will improve the accuracy, efficiency, and reliability of dynamic analysis. This is of great importance because the noise prediction of a complex structure rests substantially on the accuracy of the numerical procedures which are used to analyze them.