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Expansion of Conforming to Interface Structured Adaptive Mesh Refinement Algorithm to Higher Order Elements and Crack Propagation

Mohamadsalehi, Mohamad
http://rave.ohiolink.edu/etdc/view?acc_num=osu1649430618569018

Abstract Details

2022, Doctor of Philosophy, Ohio State University, Mechanical Engineering.
A modified version of the Conforming to Interface Structured Adaptive Mesh Refinement (CISAMR) algorithm is presented for the construction of higher order Lagrangian and NURBS-enhanced (NE) finite element meshes. CISAMR non-iteratively transforms a structured grid into a conforming mesh with an upper bound of three on aspect ratios of resulting elements. In this thesis, we introduce new algorithmic aspects for generating higher-order Lagrangian and NE meshes using CISAMR. For each type of element, a comprehensive study is then provided on the performance of first, second, and third-order meshes for solving linear elastic problems with smooth and oscillatory curvilinear edges. In these examples, local gradient recovery error, computational cost, and implementation complexity are used as performance metrics. Outcomes of this numerical study are used as a case study to elucidate some of the common sources of bias in interpreting or presenting results. In particular we show how bias, whether purposeful or not, could lead to misleading conclusions regarding the performance of a numerical technique that could even contradict the actual situation. In the next part, we expand the CISAMR algorithm for modeling complex two-dimensional (2D) crack growth problems involving contact/friction along the crack surface and interaction between multiple cracks. The CISAMR algorithm transforms a structured mesh into a high-quality conforming mesh non-iteratively, which is an attractive feature for modeling the evolution of the crack geometry with minimal changes to the underlying mesh structure. To model such problems, the mesh structure is first adaptively refined and updated near the crack tip to form a spider-web pattern of elements for the accurate approximation of the energy release rate and thereby predicting the new crack path. In each step of the crack advance simulation, a small subset of elements in the vicinity of the crack tip detected by employing a tree data structure and then deleted/regenerated to simulate the crack growth. The construction of a high-quality mesh with low element aspect ratios in the algorithm allows the use of an explicit dynamic solver, which is essential to simulate the nonlinear response of the problem caused by contact forces along crack faces. Several benchmark fracture problems are presented to study the accuracy of the proposed algorithm, as well as two more complex problems to demonstrate its ability for modeling interaction of multiple growing cracks with one another and with embedded heterogeneities in the domain.
Soheil Soghrati, Dr (Advisor)
David Talbot, Dr (Committee Member)
Rebecca Dupaix, Dr (Committee Member)
135 p.
Mechanical Engineering
higher-order mesh, NURBS enhanced element, crack growth, interaction integral, mesh generation

Recommended Citations

Citations

  • Mohamadsalehi, M. (2022). Expansion of Conforming to Interface Structured Adaptive Mesh Refinement Algorithm to Higher Order Elements and Crack Propagation [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1649430618569018

    APA Style (7th edition)

  • Mohamadsalehi, Mohamad. Expansion of Conforming to Interface Structured Adaptive Mesh Refinement Algorithm to Higher Order Elements and Crack Propagation. 2022. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1649430618569018.

    MLA Style (8th edition)

  • Mohamadsalehi, Mohamad. "Expansion of Conforming to Interface Structured Adaptive Mesh Refinement Algorithm to Higher Order Elements and Crack Propagation." Doctoral dissertation, Ohio State University, 2022. http://rave.ohiolink.edu/etdc/view?acc_num=osu1649430618569018

    Chicago Manual of Style (17th edition)

osu1649430618569018
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This open access ETD is published by The Ohio State University and OhioLINK.