Matlab Progress 5

Matlab Progress 5

Mohr circle :

By this program, you can draw Mohr circle and the Maximum shearing stress through inserting the normal stresses in the x-direction, the y-direction, and shearing stress.

 

Hint:

You need to (Circle .m) to operate the (Mohr circle .m) as it’s just function. For inserting data, the direction of shearing stress (its sign is positive at clockwise and is negative at anticlockwise) .

COMPOSITE MATERIALS REVOLUTIONISE AEROSPACE ENGINEERING - PT.2

COMPOSITE MATERIALS REVOLUTIONISE

AEROSPACE ENGINEERING - PT.2

Note: to read Part 1 Press Here.

AIRFRAME USAGE:

In order to derive maximum benefit from the use of carbon composites, it is essential to direct the fibers in the direction of the main stress. For example, the wing of an aircraft bends during take-off, landing and flight, meaning that it is subject to stress across its span. To support this, engineers orient up to 60% of the fibers along the wing skins and the span-wise internal stiffeners. In addition, wing skins are subject to parallel stresses known as shear stresses – to combat this, plies are directed at 45°. Components inside the wing, such as spars and ribs that are designed to bear shear stresses, are made of up to 80% of 45° plies. In this way, the direction at which the plies are laid ensures that material volume, and hence weight, is kept to a minimum consistent with adequate strength. In terms of the impact on the work of structural engineers, that caused by the advent of CFRP has been considerable – they can now effectively choose the stiffness characteristics of the material they are using. Taking this a step further, engineers are also collaborating with aerodynamicists to explore ‘aero-elastic tailoring’. Aircraft wings are designed in the knowledge that their shape impacts on their lift and load distribution, but also that lift and load distribution will alter their shape. By employing aero-elastic tailoring, structures engineers can generate wing designs that deflect under increases in loading in such a way as to moderate the internal load increase. CFRP is peculiarly amenable to this type of design because, by orienting fibres in specific directions, the stiffness characteristics of a laminate can be modified to give precisely the response to increased load that is required.

THE DESIGN CHALLENGES:

The foregoing description of carbon composites might lead one to question whether all of this is too good to be true: surely this wonder material must have some Achilles' heel? Indeed, there are several obstacles to achieving the low weight and low cost that the headline figures promise. Engineers are overcoming the difficulties progressively through improved design and novel manufacturing processes, but the current state of development sees engineers of all disciplines searching for the best answers .Structural engineers are faced with worries regarding damage tolerance and de-lamination, but they must also contend with the less forgiving nature of the new materials when compared with metals. Metals have the desirable quality that they exhibit plasticity: under high loads they undergo permanent deformation (i.e. they bend or stretch) before they break. As a result, a metallic structure can absorb everyday small impacts (leading to dents) with very little reduction in its basic strength. Plasticity allows loads in highly stressed regions to be re-distributed to regions of lower stress, ensuring that any stress concentrations inherent in a design do not lead to premature structural failure. Carbon/epoxy composites, by contrast, exhibit little or no plasticity. Consequently, small in-service impacts tend to create local breakdowns of the epoxy matrix, leading to a weakening of the laminate in the area of the impact. In addition, stress concentrations in a composite design can cause sudden structural failure at high load; the process would be incremental with a similar design in metal because the load would be redistributed. Structural engineers combat this lack of damage tolerance by assuming much lower stress values than theoretically necessary when they are designing, and they have had to accept an increase in the complexity of their strength calculations to accommodate the greater sensitivity of CFRP at high loads.

MANUFACTURING CHALLENGES:

Manufacturing engineers are, similarly, wrestling with unfamiliar difficulties. Problems with wrinkling of the fibers in the fabrication process, resulting in a loss of stiffness and strength in the finished component, are addressed only by imposing strict constraints on the geometry of structural features. The spectre of void formation in the resin matrix caused by a lack of consolidation of the plies during the curing process – reminiscent of Swiss cheese – creates further geometric constraints. As a consequence, engineers working with composites have realised that designing with manufacture specifically in mind is equally as important as designing for the strength/weight ratio.These issues are a small selection from a list that includes topicsas diverse as the drilling of holes in the assembly of mixed composite/metallic components to the provision of electrical diverter strips to satisfy lightning strike requirements for the finished airframe. So, the widespread introduction of CFRP must be implemented in an intelligent way.

APPLICATIONS:

Following the Airbus lead with its A380, a number of current large aircraft development programmes are looking to use composites more extensively within the wings and fuselage. The Boeing 787 ‘Dreamliner’, for example, may eventually be made of as much as 50% composite materials. This revolutionary aircraft uses a novel process of ‘winding’ composite layers, like the winding of a cotton reel, in the fabrication of large, joint-less, fuselage sections. Meanwhile the Airbus A400M, the next generationof military airlifter expected to make its first flight later this year, similarly has wings made from carbon fibre composites. This aircraft is designed to withstand the severe loads associated with operations from informal landing strips like deserts and fields, and it benefits from the superior fatigue resistance of carbon composites. The design intent is that A400M aircraft will spend less time in the maintenance hanger and more time flying missions. Beyond these aircraft, the indications are that the next generation of single-aisle airliners, ubiquitous throughout the world fleet in making 1,000-3,000 nautical mile flights with payloads of 100-180 passengers, will employ carbon composites extensively in their airframe structure.

FUTURE USES:

The environmental case for developing our understanding and increasing our exploitation of composites is compelling. The Stern Review, 2006, identified that 1.6% of global greenhouse gas emissions come from aviation but that the demand for air travel will rise with our income. To combat the environmental threat that aviation poses, theAdvisory Council for Aeronautical Research in Europe in 2002 laid out targets to reduce the emission of CO2 (an important greenhouse gas) from an aircraft by 50% by 2020. The reduction of airframe weight through the extensive use of carbon composites is just one of a range of technologies that must be deployed to meet such a challenging target.To meet the challenge that the widespread use of composite materials throws up, the civil aerospace community in the UK has launched the NextGeneration Composite Wing (NGCW) research programme, which seeks to answer some of the questions – see panel above. The environmental obstacle that confronts the aviation industry is, perhaps, the greatest it has faced in its 100 year history, the adoption of CFRP being one facet of the industry’s plan to surmount it. The NGCW programme should see the UK aerospace industry well placed to be in the vanguard of the intelligent application of these very promising materials.

Shear & Deflection Videos

Shear Test

Hiperestatic shear beam test

Scot Nommensen's Big Beam' Shear Failure

Calculating the Deflection of a Beam

Matlab Progress 4

Matlab Progress 4 

In this term, we change our knowledge about MATLAB (GUI) seeking to get the best away to reach the correct answer and updating the solving methods in the previous term. Through this term, we changed the design from 2 to 3 times to get the stylist form to attract the User to access his desired answer.

What happened in this term?

We divide the beams to two types:

• Simply supported beam
• Cantilever beam

With our problem, you can calculate:

• Reaction.
• Number of moments, disturbed loads, and external concentrated loads.
• Drawing Shear –bending moment diagram (to get any data at any distance!!)
• Maximum stress.

The initial design  - click to enlarge

In addition to the previous required, we can get:

• Vertical shear.
• Horizontal shear.
• Bending moment.
• Stress at any distance.

What we updated in this term?

By collecting information and data about the ADVABCED MATLAB!!!

We can update:

• Centroid 
• Centroid Moment of inertia. 
• Calculating the first moment of area.

Note : the Program will be released here within days, Thanks for your patience.

Contact us:

Email: aero.matlab@yahoo.com

Facebook: AERO103.MATLAB@groups.facebook.com

Blog: aero103.blogspot.com

shear and bending diagrams >>[integrating& singularity]

deflection4

chapter_transformation of plane stress..[mit]

trans

chapter(7)_transformation of beams (1)

by>> www.efunda.com

Mohr's Circle

Introduced by Otto Mohr in 1882, Mohr's Circle illustrates principal stresses and stress transformations via a graphical format,

The two principal stresses are shown in red, and the maximum shear stress is shown in orange. Recall that the normal stesses equal the principal stresses when the stress element is aligned with the principal directions, and the shear stress equals the maximum shear stress when the stress element is rotated 45° away from the principal directions.

As the stress element is rotated away from the principal (or maximum shear) directions, the normal and shear stress components will always lie on Mohr's Circle.

Mohr's Circle was the leading tool used to visualize relationships between normal and shear stresses, and to estimate the maximum stresses, before hand-held calculators became popular. Even today, Mohr's Circle is still widely used by engineers all over the world.

Derivation of Mohr's Circle

To establish Mohr's Circle, we first recall the stress transformation formulas for plane stress at a given location,

Using a basic trigonometric relation (cos22q + sin22q = 1) to combine the two above equations we have,

This is the equation of a circle, plotted on a graph where the abscissa is the normal stress and the ordinate is the shear stress. This is easier to see if we interpret sx and sy as being the two principal stresses, and txy as being the maximum shear stress. Then we can define the average stress, savg, and a "radius" R (which is just equal to the maximum shear stress),

The circle equation above now takes on a more familiar form,

The circle is centered at the average stress value, and has a radius R equal to the maximum shear stress, as shown in the figure below,

Cylindrical Pressure Vessel

Consider a cylindrical pressure vessel with radius r and wall thickness t subjected to an internal gage pressure p.

The coordinates used to describe the cylindrical vessel can take advantage of its axial symmetry. It is natural to align one coordinate along the axis of the vessel (i.e. in the longitudinal direction). To analyze the stress state in the vessel wall, a second coordinate is then aligned along the hoop direction.

With this choice of axisymmetric coordinates, there is no shear stress. The hoop stress sh and the longitudinal stress sl are the principal stresses.

To determine the longitudinal stress sl, we make a cut across the cylinder similar to analyzing the spherical pressure vessel. The free body, illustrated on the left, is in static equilibrium. This implies that the stress around the wall must have a resultant to balance the internal pressure across the cross-section.

Applying Newton's first law of motion, we have,

and <this strees is a n axial stress&get;

· To determine the hoop stress sh, we make a cut along the longitudinal axis and construct a small slice as illustrated on the right.

The free body is in static equilibrium. According to Newton's first law of motion, the hoop stress yields,

chapter (7)_transformation of plane stress (2)

By www.efunda.com

Calculator Introduction of the stresses


Given the stresses at a space point in the body, sx, sy, and txy, this calculator computes the stresses of the same space point in a rotated coordinate system, sx', sy', and tx'y'.

Equations behind the Calculator

The following coordinate transformation equations were used,

principale stresses

Given the stress components sx, sy, and txy, this calculator computes the principal stresses s1, s2, the principal angle qp, the maximum shear stress tmax and its angle qs. It also draws an approximate Mohr's cirlce for the given stress state.

The Mohr's circle associated with the above stress state is similar to the following figure. However, the exact loaction of the center sAvg, the radius of the Mohr's circle R, and the principal angle qp may be different from what are shown in the figure.

Equations behind the Calculator


The formulas used in this calculator are,

chapter(7)_transformation of plane stress (2)

Calculator Introduction of the stresses


Given the stresses at a space point in the body, sx, sy, and txy, this calculator computes the stresses of the same space point in a rotated coordinate system, sx', sy', and tx'y'.

Equations behind the Calculator

The following coordinate transformation equations were used,

principale stresses

Given the stress components sx, sy, and txy, this calculator computes the principal stresses s1, s2, the principal angle qp, the maximum shear stress tmax and its angle qs. It also draws an approximate Mohr's cirlce for the given stress state.

The Mohr's circle associated with the above stress state is similar to the following figure. However, the exact loaction of the center sAvg, the radius of the Mohr's circle R, and the principal angle qp may be different from what are shown in the figure.

Equations behind the Calculator


The formulas used in this calculator are,

Chapter(7)_ Transformation of plane stress

Mohr's Circle

Introduced by Otto Mohr in 1882, Mohr's Circle illustrates principal stresses and stress transformations via a graphical format,

The two principal stresses are shown in red, and the maximum shear stress is shown in orange. Recall that the normal stesses equal the principal stresses when the stress element is aligned with the principal directions, and the shear stress equals the maximum shear stress when the stress element is rotated 45° away from the principal directions.

As the stress element is rotated away from the principal (or maximum shear) directions, the normal and shear stress components will always lie on Mohr's Circle.

Mohr's Circle was the leading tool used to visualize relationships between normal and shear stresses, and to estimate the maximum stresses, before hand-held calculators became popular. Even today, Mohr's Circle is still widely used by engineers all over the world.

Derivation of Mohr's Circle

To establish Mohr's Circle, we first recall the stress transformation formulas for plane stress at a given location,

Using a basic trigonometric relation (cos22q + sin22q = 1) to combine the two above equations we have,

This is the equation of a circle, plotted on a graph where the abscissa is the normal stress and the ordinate is the shear stress. This is easier to see if we interpret sx and sy as being the two principal stresses, and txy as being the maximum shear stress. Then we can define the average stress, savg, and a "radius" R (which is just equal to the maximum shear stress),

The circle equation above now takes on a more familiar form,

The circle is centered at the average stress value, and has a radius R equal to the maximum shear stress, as shown in the figure below,

Cylindrical Pressure Vessel

Consider a cylindrical pressure vessel with radius r and wall thickness t subjected to an internal gage pressure p.

The coordinates used to describe the cylindrical vessel can take advantage of its axial symmetry. It is natural to align one coordinate along the axis of the vessel (i.e. in the longitudinal direction). To analyze the stress state in the vessel wall, a second coordinate is then aligned along the hoop direction.

With this choice of axisymmetric coordinates, there is no shear stress. The hoop stress sh and the longitudinal stress sl are the principal stresses.

To determine the longitudinal stress sl, we make a cut across the cylinder similar to analyzing the spherical pressure vessel. The free body, illustrated on the left, is in static equilibrium. This implies that the stress around the wall must have a resultant to balance the internal pressure across the cross-section.

Applying Newton's first law of motion, we have,

and <this strees is a n axial stress&get;

· To determine the hoop stress sh, we make a cut along the longitudinal axis and construct a small slice as illustrated on the right.

The free body is in static equilibrium. According to Newton's first law of motion, the hoop stress yields,