Bachelor's Thesis

Computational modelling of a compound rotating circular disc with uniform temperature distribution

Final Thesis 6.28 MB Appendix 44.82 kB

Author of thesis: Bc. Nichole Ann Philip

Acad. year: 2025/2026

Supervisor: Ing. Miroslav Hrstka, Ph.D.

Reviewer: Ing. Oldřich Ševeček, Ph.D.

Abstract:

This thesis deals with the computational modelling of a compound rotating circular disc sub
jected to a uniform temperature field. The main objective was to analyze the stress and de
formation behaviour of the compound rotating disc composed of two, three, and four materials
under thermo-mechanical loading conditions. First, the theoretical formulation of the rotating
disc problem was established using elasticity and equilibrium equations in cylindrical coordi
nates. Based on these relations, analytical expressions for radial stress, circumferential stress,
and radial displacement were derived and were used to create analytical models for compound
disc configurations. A computational model based on the analytical formulation was built in
Python for evaluating the mechanical response of the considered disc configurations. In parallel,
finite element models were also created using ANSYS Mechanical APDL to simulate the thermo
mechanical behaviour of the compound rotating discs under rotational loading, thermal loading
and interface contact conditions. The obtained analytical and finite element results showed
strong agreement in terms of stress and displacement distributions, validating the developed
analytical approach. Additional parametric studies were performed to evaluate the influence
of interference values, angular velocity, and temperature field on the stresses and deformation
of the disc. The results confirmed that the developed analytical and finite element approaches
provide reliable tools for assessing the thermo-mechanical behaviour of compound rotating discs
and may support future engineering analysis and optimization of rotating structures operating
under combined thermal and mechanical loading.

Keywords:

Rotating disc; stress; thermal strain; angular velocity; finite element modelling; compound disc

Date of defence

17.06.2026

Result of the defence

Defended (thesis was successfully defended)

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Grading

A

Process of defence

The student presented the committee with the progress of the work, the results and conclusions of the thesis, and answered the reviewer's questions. Doc. Šremr discussed a specific equation from the thesis and asked whether it came from the literature. The student confirmed that it did. Prof. Novotný asked whether the analytical equations in the thesis had been derived using AI or manually. The student stated that she had derived them manually. Doc. Charvát asked why several materials had been used within a single disc. According to the student, using different materials makes sense because of their differing strength. Doc. Jan asked for a physical explanation of why the stresses in the disc are discontinuous. The student explained and described the graphs. A discussion followed on the materials used and their properties, and on the limits of the model.

Language of thesis

English

Faculty

Department

Study programme

Fundamentals of Mechanical Engineering (B-STI-A)

Composition of Committee

doc. Ing. František Lízal, Ph.D. (člen)
doc. Ing. Vít Jan, Ph.D. (člen)
doc. Ing. Jiří Šremr, Ph.D. (člen)
prof. Ing. Pavel Novotný, Ph.D. (předseda)
doc. Ing. Pavel Charvát, Ph.D. (místopředseda)

Supervisor’s report
Ing. Miroslav Hrstka, Ph.D.

Ms. Philip dealt in her thesis with the computational modelling of a compound circular disc subjected to uniform temperature field. In the first part, the analytical formulae for a cylindrical body were used to extract displacement and stress field. Three different configurations were analysed – a disc composed from two, three and four materials. In the second section, the plane finite element model in the ANSYS software was created and its outputs were compared with the analytical solutions. Finally, some parametrical studies were performed to prove the validity of the theory and applicability to the problem of the rotating heated body. Ms. Philip attended the consultations regularly, worked proactively and learned programming in Python and scripting in the ANSYS apdl language. I claim that the goals of the thesis have been achieved and I recommend the thesis for defence with a final grade A.
Evaluation criteria Grade
Fulfilment of requirements and objectives of assignment A
Working process, extent and suitability of applied methods A
Scholarly contribution and originality B
Ability to interpret achieved results and draw conclusions A
Applicability of results in practice or theory A
Logical arrangement of thesis and its layout A
Grafic layout, used style and language level A
Work with used sources including quotations A
Student's independence when working on the topic A

Grade proposed by supervisor: A

Reviewer’s report
Ing. Oldřich Ševeček, Ph.D.

The submitted bachelor’s thesis deals with the computational modelling of compound rotating circular discs subjected to thermo-mechanical loading. The topic is relevant to recent engineering practice, particularly in the design and analysis of rotating components used in turbines, turbochargers, and aerospace applications. The work compares analytical calculations with numerical simulations using finite element method in ANSYS Mechanical.
     The theoretical part provides an introduction to the mechanics of rotating discs and presents the derivation of the governing equations based on elasticity theory. The author demonstrates a good understanding of the fundamental principles of stress, strain, and thermoelastic behaviour. The formulation is logically structured and leads systematically to the development of analytical models for compound discs consisting of two, three, and four parts. However, some equations are introduced without sufficient explanation of intermediate steps. For example, the transition between the governing differential equation and the final stress-displacement relations could be discussed in more details. I miss also some explanation from where the term with rotational velocity in Eq.3.16 originated. Author also use for angular velocity units RPM which is not correct – should be rad/s. All analytical formulas require input in rad/s so it is thus a question what was really considered in the calculations.
      On the other hand a stronger aspect of the thesis lays in the practical part, in the development of analytical computational models and their comparison with finite element simulations performed in ANSYS APDL. The author successfully implemented the mathematical formulation and verified the analytical results using FEM analysis. The agreement between both approaches indicates that the developed models are correct and applicable for the considered problem. Nevertheless, the FEM section would further benefit from a more detailed discussion of e.g. mesh quality, convergence, and modelling assumptions or contact settings, which are missing. Also mixing boundary conditions together with deformation conditions is not fully correct.
     The discussion of results is well organized and demonstrates the student’s ability to evaluate the influence of material composition, overlaps between disc parts, angular velocity, and temperature on the stress and displacement fields. Although the conclusions are generally supported by the results, the discussion is occasionally descriptive and could provide a more detailed engineering interpretation.
      From a stylistic perspective, the thesis is understandable and logically structured. The technical terminology is mostly used correctly (except e.g. the above mentioned angular speed in RPM units), the text contains some grammatical inaccuracies, repetitive formulations, and minor language issues that reduce its overall quality. The bibliography contains relevant sources and their citation is generally satisfactory.
      Overall, the thesis fulfills the assigned objectives and demonstrates that the student is capable of applying theoretical knowledge to solve a practical engineering problem using both analytical and numerical methods. Despite some small shortcomings in the theoretical part, depth of discussion or language quality, the work represents a solid bachelor-level thesis. I thus recommend the work for a defence and I evaluate it by grade "B".
Evaluation criteria Grade
Fulfilment of requirements and objectives of assignment A
Working process, extent and suitability of applied methods B
Scholarly contribution and originality B
Ability to interpret achieved results and draw conclusions B
Applicability of results in practice or theory B
Logical arrangement of thesis and its layout B
Grafic layout, used style and language level B
Work with used sources including quotations B
Topics for thesis defence:
  1. Would it be possible to consider also temperature gradient over the disc radius in the analytical calculations? How the analytical expressions will change?
  2. Which contact formulation (type) was used in ANSYS APDL and how did you model the overlap between bodies using the contact?
  3. Why you didn’t use a 2D FE model with rotational symmetry (cross-sectional cut of the disc) instead – to capture correctly real thickness of the disc and stresses in Z-direction which will not be generally zero due to a mismatch in CTE between adjacent discs?
  4. Which units you really substituted during calculations for angular velocity "omega"?

Grade proposed by reviewer: B

Responsibility: Mgr. et Mgr. Hana Odstrčilová