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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