Lecture_Equilibrium_Compatability_Plane_Elastic_Problems

Lecture_Equilibrium_Compatability_Plane_Elastic_Problems -...

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Class Workbook and Handouts - MME 412: Mechanics of Materials Prepared by: Kumar V. Singh -57- Generalized Stress Strain Relations:

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Class Workbook and Handouts - MME 412: Mechanics of Materials Prepared by: Kumar V. Singh -58-
Class Workbook and Handouts - MME 412: Mechanics of Materials Prepared by: Kumar V. Singh -59- Equilibrium and Compatibility Equations: Figure 2.4-1 [1]

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Class Workbook and Handouts - MME 412: Mechanics of Materials Prepared by: Kumar V. Singh -60- Equilibrium Equations Equilibrium Equations for the case of Plane Stress
Class Workbook and Handouts - MME 412: Mechanics of Materials Prepared by: Kumar V. Singh -61- Compatibility Equations Equilibrium equations ensure that any segment of the body together with its corresponding internal force distribution must maintain the segment in static equilibrium. Stress distribution is said to be acceptable when it ensures a piecewise continuous deformation distribution of the body ( Compatibility ): has to be compatible with boundary conditions along the structure has no holes, no overlapping etc. at any point Conditions for compatibility:

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Class Workbook and Handouts - MME 412: Mechanics of Materials Prepared by: Kumar V. Singh -62- (See Additional Handout from the Book of Solecki and Conant on Compatibility)
Class Workbook and Handouts - MME 412: Mechanics of Materials Prepared by: Kumar V. Singh -63- Example:

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Class Workbook and Handouts - MME 412: Mechanics of Materials Prepared by: Kumar V. Singh
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Lecture_Equilibrium_Compatability_Plane_Elastic_Problems -...

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