The field of structural design optimization is one with great breadth and depth in many engineering applications. From the perspective of a designer, three distinct numerical methodologies may be employed. These include size, shape, and topology optimization, in which the ordering typically (but not always) corresponds to the order of increasing complexity and computational expense. This, of course, depends on the particular problem of interest and the selected numerical methods. The primary focus of this research employs density-based topology optimization with the goal of improving structural resistance to failure.
Beginning with brittle fracture, two topology optimization based formulations are proposed in which low weight designs are achieved with substantially increased fracture resistance. In contrast to the majority of the current relevant literature which favors stress constraints with linear elastic physics, we explicitly simulate brittle fracture using the phase field method during the topology optimization procedure. In the second formulation, a direct comparison is made against results obtained using conventional stress-constrained topology optimization and the improved performance is numerically demonstrated. Multiple enhancements are proposed including a numerical efficiency gain based on the Schur-complement during the analytical sensitivity analysis and a new function which provides additional path information to the optimizer, making the gradient-based optimization problem more tractable in the presence of brittle fracture physics.
Subsequently, design for ductile failure and buckling resistance is addressed and a numerically efficient topology optimization formulation is proposed which may provide significant design improvements when ductile materials are used and extreme loading situations are anticipated. The proposed scheme is examined regarding its impact on both the peak load carrying capacity of the structure and the amount of external work required to achieve this peak load, past which the structure may no longer be able to support any increase in the external force. The optimized structures are also subjected to a post-optimization verification step in which a large deformation phase field fracture model is used to numerically compare the performance of each design. Significant gains in structural strength and toughness are demonstrated using the proposed framework.
Additionally, the failure behavior of 3D-printed polymer composites is investigated, both numerically and experimentally. A large deformation phase field fracture model is derived under the assumption of plane-stress for numerical efficiency. Experimental results are compared to numerical simulations for a composite system consisting of three stiff circular inclusions embedded into a soft matrix. In particular, we examine how geometric parameters, such as the distances between inclusions and the length of initial notches affect the failure pattern in the soft composites. It is shown that the mechanical performance of the system (e.g. strength and toughness) can be tuned through selection of the inclusion positions which offers useful insight for material design.
Finally, a size optimization technique for a cardiovascular stent is proposed with application to a balloon expandable prosthetic heart valve intended for the pediatric population born with Congenital Heart Disease (CHD). Multiple open heart surgical procedures are typically required in order to replace the original diseased valve and subsequent prosthetic valves with those of larger diameter as the patient grows. Most expandable prosthetic heart valves currently in development to resolve this issue do not incorporate a corresponding expandable conduit that is typically required in a neonate without a sufficiently long Right Ventricular Outflow Tract (RVOT). Within the context of a particular design, a numerical methodology is proposed for designing a metallic stent incorporated into the conduit between layers of polymeric glue. A multiobjective optimization problem is solved, not only to resist the retractive forces of the glue layers, but also to ensure the durability of the stent both during expansion and while subject to the anticipated high cycle fatigue loading. It is demonstrated that the surrogate-based optimization strategy is effective for understanding the trade-offs between each performance metric and ultimately efficiently arriving at a single optimized design candidate. Finally, it is shown that the desired expandability of the device from 12mm to 16mm inner diameter is achievable, effectively eliminating at least one open heart surgical procedure for certain children born with CHD.
| Identifer | oai:union.ndltd.org:columbia.edu/oai:academiccommons.columbia.edu:10.7916/d8-rfmz-6x23 |
| Date | January 2021 |
| Creators | Russ, Jonathan Brent |
| Source Sets | Columbia University |
| Language | English |
| Detected Language | English |
| Type | Theses |
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