Lecture #13Concluding lecture
PLACE OF STRUCTURAL ANALYSIS IN THE ASSURANCE OF AIRCRAFT STRENGTH
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Mechanicsof Materials
StructuralAnalysis
Strengthof Aircraft
Strength of local zones
Methods for analysisof general stress state
Methods for calculationof loading and strength
Structures
Constrained (fixed) a) stable (immovable)
b) unstable (movable)
Unconstrained (free)a) stable (invariable)
b) unstable (variable)
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CLASSIFICATION OF STRUCTURAL ANALYSIS PROBLEMS
Stable structures
Statically determinate Statically indeterminate
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CLASSIFICATION OF STRUCTURAL ANALYSIS PROBLEMS
Methods of classification
Structural analysis Kinematical analysis
Statical analysis
Statically determinate Statically 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 manufacture Hard to manufacture
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CLASSIFICATION OF STRUCTURAL ANALYSIS PROBLEMS
MAIN METHODS COVERED IN SECOND SEMESTER
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Methods of structural analysis
Analytical methods Numerical methods(finite element method)
Method of joints
Method of sections
Force method
Displacement method (slope-deflection method)
Matrix methods
For statically indeterminate
structures
For statically determinate structures
METHODS OF STRUCTURAL ANALYSIS
Analytical methods Numerical 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
hardware7
FLOWCHART OF SOLUTION USING FORCE METHOD
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Classificationof the problem
Basic system
Loaded andunit states
Redundant constraints are removed
In loaded state, external load is applied. In unit states, unit force is applied instead of constraint.
Canonical equations
Total stress state
Forces in removed constraints are determined
Displacements corresponding to removed constraints are
determined for each state
EXAMPLE OF FORCE METHOD APPLICATION #3
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EXAMPLE OF FORCE METHOD APPLICATION #3(NUMERICAL SOLUTION)
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FLOWCHART OF DISPLACEMENT METHOD
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Classificationof the problem
Basic system
Loaded andunit states
Free DOFs are removed (constrained)
In loaded state, external load is applied. In unit states, unit displacements are applied.
Canonical equations
Total stress state
Actual displacements of introduced constraints are
determined
Reaction forces in introduced constraints are determined for
each state
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SWEPTBACK WING ROOT TRIANGLE
DESIGN MODEL OF SWEPTBACK WING
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EXAMPLEFOR A TOTALSTRESSSTATE
TOPIC OF THIS SEMESTER
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Frame and truss structures, mostly planar problems.
TOPIC OF LAST SEMESTER
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Thin-walled stiffened structures, mostly spatial problems
3D model by MiljanD
TYPICAL STRESS DISTRIBUTIONS IN CROSS SECTION
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, MPaz
, MPaMises
, MPaxz
2 23Mises z xz
SHEAR STRESSES RELATED QUESTIONS
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- 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.
BUCKLING MODES OF AIRCRAFT PANEL
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