I am writing a proposal for my PhD. In the proposal I have included a chapter titled “Actuator Design”. Within that same chapter, can I include a section with the same name as that chapter, meaning the very same “Actuator Design” as I’ve already used?
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You can include whatever sections you like; the real question is whether your advisor or committee will approve what you write. If the structure is made more logical, organized, and clear by having a section called “Actuator Design” within a chapter called “Actuator Design”, then go ahead and use such a section.
There are cases where structure would not be improved by such a section: for example, if the section were at the immediate beginning of the chapter and were introductory and general. In a case like that, dispense with the “Actuator Design” section name, and present its information at the chapter level. Then add section headings as necessary following that introduction.
You also might want to rename the chapter or the section. If “Actuator Design” is only a section of a chapter, then the chapter must actually cover more topics than “Actuator Design”, or the section must cover less. For example, if your “Actuator Design” chapter has two sections, called “Actuator Design – Overview” and “Actuator Design – Details”, perhaps just rename the sections to “Overview” and “Details”.
It's a poor style - why make it a section while the chapter should contain it, what are other contents of the chapter if one section covers its whole title.
But you can give it a subtitle:
If your chapter is to contain only one section, which covers the entire subject of the chapter, don't make any section and start writing the content directly under the chapter level.
Yes you can.
But I'd like to add, you'd need to think and question why you would have a Chapter Head and a Section Head as the same name.
Normal practice would be to use chapter heads as a generic title as to what that particular chapter contains. Section heads would normally go into even more specific detail about the contents of the chapter.
Chapter Title - Actuator Design
Section Heading - Design Parameters, Design Specifications, Design limiting factors, and so on.