1.033/1.57: Mechanics of Material Systems 1.033/1.57 Mechanics of Material Systems (Mechanics and...
-
Upload
charles-hutchison -
Category
Documents
-
view
228 -
download
3
Transcript of 1.033/1.57: Mechanics of Material Systems 1.033/1.57 Mechanics of Material Systems (Mechanics and...
![Page 1: 1.033/1.57: Mechanics of Material Systems 1.033/1.57 Mechanics of Material Systems (Mechanics and Durability of Solids I) Franz-Josef Ulm Lecture: MWF1.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551502f455034693478b6614/html5/thumbnails/1.jpg)
1.033/1.57
Mechanics of Material Systems(Mechanics and Durability of Solids I)
Franz-Josef Ulm
Lecture: MWF1 // Recitation: F3:00-4:30
![Page 2: 1.033/1.57: Mechanics of Material Systems 1.033/1.57 Mechanics of Material Systems (Mechanics and Durability of Solids I) Franz-Josef Ulm Lecture: MWF1.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551502f455034693478b6614/html5/thumbnails/2.jpg)
Part II: Momentum Balance,
Stresses and Stress States
3. Momentum Balance
![Page 3: 1.033/1.57: Mechanics of Material Systems 1.033/1.57 Mechanics of Material Systems (Mechanics and Durability of Solids I) Franz-Josef Ulm Lecture: MWF1.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551502f455034693478b6614/html5/thumbnails/3.jpg)
Content 1.033/1.57Part I. Deformation and Strain 1 Description of Finite Deformation 2 Infinitesimal DeformationPart II. Momentum Balance and Stresses 3 Momentum Balance 4 Stress States / Failure CriterionPart III. Elasticity and Elasticity Bounds 5 Thermoelasticity, 6 Variational MethodsPart IV. Plasticity and Yield Design 7 1D-Plasticity – An Energy Approac 8 Plasticity Models 9 Limit Analysis and Yield Design
![Page 4: 1.033/1.57: Mechanics of Material Systems 1.033/1.57 Mechanics of Material Systems (Mechanics and Durability of Solids I) Franz-Josef Ulm Lecture: MWF1.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551502f455034693478b6614/html5/thumbnails/4.jpg)
Body & Surface Forces
![Page 5: 1.033/1.57: Mechanics of Material Systems 1.033/1.57 Mechanics of Material Systems (Mechanics and Durability of Solids I) Franz-Josef Ulm Lecture: MWF1.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551502f455034693478b6614/html5/thumbnails/5.jpg)
Hypothesis of local contact forces=Action-Reaction ‘Law’
![Page 6: 1.033/1.57: Mechanics of Material Systems 1.033/1.57 Mechanics of Material Systems (Mechanics and Durability of Solids I) Franz-Josef Ulm Lecture: MWF1.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551502f455034693478b6614/html5/thumbnails/6.jpg)
Tetrahedron Lemma: Stress vector T(n)
![Page 7: 1.033/1.57: Mechanics of Material Systems 1.033/1.57 Mechanics of Material Systems (Mechanics and Durability of Solids I) Franz-Josef Ulm Lecture: MWF1.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551502f455034693478b6614/html5/thumbnails/7.jpg)
Cauchy Stresses σij and Stress Vector T(n)
Components of σij Stress Vector Tj= σijnj
![Page 8: 1.033/1.57: Mechanics of Material Systems 1.033/1.57 Mechanics of Material Systems (Mechanics and Durability of Solids I) Franz-Josef Ulm Lecture: MWF1.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551502f455034693478b6614/html5/thumbnails/8.jpg)
Exercise: Two-Layer Soil Substratum
![Page 9: 1.033/1.57: Mechanics of Material Systems 1.033/1.57 Mechanics of Material Systems (Mechanics and Durability of Solids I) Franz-Josef Ulm Lecture: MWF1.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551502f455034693478b6614/html5/thumbnails/9.jpg)
Reduction Formulae
Section
=Relation between local stress and section forces and moments
Oriented Surface
PositionVector in Section
Stress Vector
![Page 10: 1.033/1.57: Mechanics of Material Systems 1.033/1.57 Mechanics of Material Systems (Mechanics and Durability of Solids I) Franz-Josef Ulm Lecture: MWF1.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551502f455034693478b6614/html5/thumbnails/10.jpg)
Momentum Balance and Symmetry of Stress Tensor
Dynamic Moment TheoremDynamic Resultant Theorem
![Page 11: 1.033/1.57: Mechanics of Material Systems 1.033/1.57 Mechanics of Material Systems (Mechanics and Durability of Solids I) Franz-Josef Ulm Lecture: MWF1.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551502f455034693478b6614/html5/thumbnails/11.jpg)
Training Set: Pressure Vessel Formula
![Page 12: 1.033/1.57: Mechanics of Material Systems 1.033/1.57 Mechanics of Material Systems (Mechanics and Durability of Solids I) Franz-Josef Ulm Lecture: MWF1.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551502f455034693478b6614/html5/thumbnails/12.jpg)
Momentum Balance in Cylinder
Radial Direction:
Coordinates
![Page 13: 1.033/1.57: Mechanics of Material Systems 1.033/1.57 Mechanics of Material Systems (Mechanics and Durability of Solids I) Franz-Josef Ulm Lecture: MWF1.](https://reader035.fdocuments.us/reader035/viewer/2022062417/551502f455034693478b6614/html5/thumbnails/13.jpg)
Vessel Formula by ReductionElements