1. Lecture #13 Concluding lecture

2. PLACE OF STRUCTURAL ANALYSIS IN THE ASSURANCE OF AIRCRAFT STRENGTH 2 Mechanics of Materials Structural Analysis Strength of Aircraft Methods for calculation of loading and strength Methods for analysis of general stress state Strength of local zones

3. 3 CLASSIFICATION OF STRUCTURAL ANALYSIS PROBLEMS

4. 4 Methods of classification Structural analysis Kinematical analysis Statical analysis

5. Statically determinateStatically indeterminate Equilibrium equations could be directly solved, and thus forces could be calculated in an easy way Equilibrium equations could be solved only when coupled with physical law and compatibility equations Stress state depends only on geometry & loading Stress state depends on rigidities Not survivable, moderately used in modern aviation (due to damage tolerance requirement) Survivable, widely used in modern aviation (due to damage tolerance property) Easy to manufactureHard to manufacture 5 CLASSIFICATION OF STRUCTURAL ANALYSIS PROBLEMS

6. MAIN METHODS COVERED IN SECOND SEMESTER 6 For statically indeterminate structures For statically determinate structures

7. METHODS OF STRUCTURAL ANALYSIS Analytical methodsNumerical methods Best for designing calculations, suit for checking calculations with certain limitations Best for checking calculations, practically effete for designing calculations Solutions exist for partial cases (specific objects) Versatile and flexible Need much work to be developed, but only simple software for application Need expensive and complex software and hardware 7

8. FLOWCHART OF SOLUTION USING FORCE METHOD 8 Classification of the problem Basic system Loaded and unit states Canonical equations Total stress state Forces in removed constraints are determined Displacements corresponding to removed constraints are determined for each state In loaded state, external load is applied. In unit states, unit force is applied instead of constraint. Redundant constraints are removed

9. EXAMPLE OF FORCE METHOD APPLICATION #3 9

10. (NUMERICAL SOLUTION) 10

11. FLOWCHART OF DISPLACEMENT METHOD 11 Classification of the problem Basic system Loaded and unit states Canonical equations Total stress state Actual displacements of introduced constraints are determined Reaction forces in introduced constraints are determined for each state In loaded state, external load is applied. In unit states, unit displacements are applied. Free DOFs are removed (constrained)

12. 12 SWEPTBACK WING ROOT TRIANGLE

13. DESIGN MODEL OF SWEPTBACK WING 13

14. EXAMPLE FOR A TOTAL STRESS STATE

15. TOPIC OF THIS SEMESTER 15 Frame and truss structures, mostly planar problems.

16. TOPIC OF LAST SEMESTER 16 Thin-walled stiffened structures, mostly spatial problems 3D model by MiljanD

17. TYPICAL STRESS DISTRIBUTIONS IN CROSS SECTION 17

18. SHEAR STRESSES RELATED QUESTIONS 18 - shear flows due to the shear force, with no torsion; - shear center; - torsion of closed contour; - torsion of opened contour, restrained torsion and deplanation; - shear flows in the closed contour under combined action of bending and torsion; - twisting angles; - shear flows in multiple-closed contours.

19. BUCKLING MODES OF AIRCRAFT PANEL 19