Hierarchical field compositions for discontinuous enrichment and system-level synthesis

Venkatakrishnan Srinivasan, Purdue University

Abstract

It is observed that fracture in large systems such as aircraft, naval or microelectronic systems occurs across multiple length scales. It is often of great interest to study the effect of loads imposed at a system (larger) length scale on crack propagation at the component (smaller) length scale. It is also of significant interest to effect geometrical and material arrangements across these length-scales to achieve a desired system-level behavior such as fracture resistance. Developing hierarchical design solutions for systems and to mitigate fracture in components is the goal of this thesis. Such a hierarchical modeling framework would enable the design of high performance systems and fracture resistant materials/structures whose applications are many, and are spread across multitude of domains. Computational methodologies for hierarchical modeling that can achieve the above stated objective do not exist in the literature. In addition, challenges such as system level synthesis, remeshing, design in the presence of cracks as well as 3-D arbitrary crack propagation need to be addressed as part of such a design framework. Thus, the specific aims of this thesis are to develop design methodologies, computational techniques, and simulation tools that go beyond analysis to enable component level synthesis in the presence of cracks and coordinated system-level synthesis. In the first part of the thesis, the theory of Hierarchical Partition of Unity Field Compositions (HPFC) is developed for component level analysis and synthesis. It is also applied for fracture analysis and for the optimal design in the presence of cracks. In the HPFC procedure, the geometrical, material and behavioral fields defined over primitive domains are composed through Boolean operations similar to the Constructive Solid Geometry Procedure of CAD. Further, an approach is developed to enrich approximations by compositions of higher dimensional fields with lower dimensional fields. This approach, which uses distance fields can enrich with specified value or gradient, discontinuity, singularity or arbitrary functions. More specifically, cracks are modeled as compositions of a continuous field with a discontinuous enrichment field. Convergence of the composed fields is ensured by developing constructions that obey the partition of unity property. Non-Uniform Rational B-Splines (NURBS) that are a common choice for modeling curves and surfaces in CAD systems are used to discretize the geometry, material, and behavioral fields (local approximations) over the primitive regions and to describe crack shapes as well as the discontinuous behavioral field corresponding to the crack. Following several validation examples, crack propagation simulations without remeshing, and example problems aimed at determining the optimal location and shape of defense holes in the presence of fracture constraints are demonstrated. In the second part of this thesis, the concept of hierarchical compositions is extended to system-level synthesis by developing a formal procedure for the coordinated synthesis of engineering systems. By using an iso-parametric or iso-geometric mapping of the geometrical model, material description and behavioral fields, a natural correspondence is established between the physical hierarchy of the system and its behavioral hierarchy. This geometry-centric philosophy, together with an appropriately defined adjoint problem allows the evaluation of arbitrary system-level functions locally on the sub-systems by capturing interactions between the subsystems without exchange of geometrical and material data (CAD models). The developed procedures are demonstrated through a detailed example involving a particulate composite material system in which the effective thermal conductivity is evaluated in a partitioned manner. A multiphysics, meshless computational framework called HiDAC is developed to implement the above mentioned methodologies. HiDAC is programmed in the JAVA language. It consists of several modules to solve a wide class of problems, which were mentioned before. In summary, this thesis is a step towards synthesis of large scale systems and components in the presence of "moving boundaries" such as cracks.

Degree

Ph.D.

Advisors

Subbarayan, Purdue University.

Subject Area

Mechanical engineering|Computer science

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