Calculating Effective Rigidities of a Laminated Composite Beam (Classical Laminate Theory)


The application of fibre-reinforced composite materials in the aerospace industry extends from commercial to military aircraft, such as the Boeing F18, B2 Stealth Bomber, AV-8B Harrier (Jones, 1998). The attractiveness of composites lies in their mechanical properties; such as weight, strength, stiffness, corrosion resistance, fatigue life. Composites are widely used for control surfaces such as ailerons, flaps, stabilizers, rudders, as well as rotary and fixed wings. That is why the analysis of composite structures is imperative for aerospace industry. The main advantage of composites is their flexibility in design. Mechanical properties of the laminate can be altered simply by changing the stacking sequence, fibre lay-up and thickness of each ply which leads to optimization in a design process.


The composite beam is modeled based on the chord-wise bending moment (about the z-axis) being small compared to the span-wise moment (about the y axis, see Figure 2). The chord-wise moment is then neglected. The composite material pertaining to this research is a unidirectional fibre reinforced composite material. The given information of any unidirectional composite material is the elastic modulus in both the longitudinal and transverse axis (see Figures 1 and 2), Poison’s ratio and the shear modulus in the principle directions.

 Effective rigidities for a solid cross-section

The reduced stiffness constants in the material principle directions are:

where T  is the transformation matrix which is used to transform the reduced stiffness constants from the principal material fibre directions to a global (x, y, z) beam coordinates.

Then, the resulting transformed reduced stiffness constants for a unidirectional or orthotropic composite from its principal directions is (Berthelot, 1999):

Both equations (above) can be merged into a single equation commonly known as the “Constitutive Equation”. The constitutive equation describes the stiffness matrix of a laminate plate. The resultant forces and moments are functions of the in-plane strains and curvatures (Berthelot, 1999).

where  is the distance from the mid-plane of the laminate (Figure 3).

For a bending-torsion coupling behaviour the chord wise moment Mx is assumed to be zero so that the kx curvature can be eliminated from (above) and then the matrix  equation (11) reduces to the following form:


The EI, GJ and K represent the effective rigidities of the beam in the global (x, y, z) coordinate system. EI, GJ, and Krepresent, respectively, the bending rigidity, torsion rigidity and bending-torsion coupled rigidity. The effective rigidities are functions of ply angle, thickness, and stacking sequence.


Six Lessons On Innovation From The Wright Brothers

When Wilbur and Orville Wright managed to build and fly an airplane, you might imagine that the world was immediately dazzled by their amazing achievement.

You’d be wrong.

As David McCullough chronicles in his excellent book The Wright Brothers, many of the “most prominent engineers, scientists, and original thinkers of the nineteenth century had been working on the problem of controlled flight,” without success. The endeavor was fraught with hazards that included “humiliating failure, injury, and, of course, death, (but also)… the inevitable prospect of being mocked as a crank, a crackpot, and in many cases with good reason.”


Lesson #1: Don’t worry about failure

John T. Daniels, who witnessed their first successful flights, said later, “It wasn’t luck that made them fly; it was hard work and common sense; they put their whole heart and soul and all their energy into an idea and they had the faith.”

Lesson #2: Have a publicity plan, but don’t expect instant success

The brothers had a preexisting plan to alert the media when they finally achieved success. It involved notifying newspapers and the Associated Press, which they did. A smattering of largely inaccurate accounts appeared in some newspapers, and the story almost instantly disappeared.

Lesson #3: Keep going, no matter what

Fortunately, the brothers were not obsessed with media attention; they were obsessed with their idea. So they kept trying to improve and test their machine.

Locals and local media either ignored them or felt sorry for them. One editor recalled, “They seemed like well-meaning, decent enough young men. Yet there they were, neglecting their business to waste their time day after day on that ridiculous flying machine.”

As they enjoyed one success after another, almost no one believed them or took notice. Today, we understand the immense importance of airplanes to our society and economy, but in those days almost no one had the imagination to take these silly inventors seriously.

Lesson #4: Accept help from strange quarters

After dozens and dozens of successful flights, the brothers were still being ignored by the media. The person who changed this was not at all what you would expect. He didn’t write for The Washington Post, The New York Times, or the AP. He was Amos Root, a deeply religious man who shared his thoughts through his company’s trade journal, Gleanings in Bee Culture.

Yes, Root’s company sold beekeeping supplies, and he had a personal interest in human flight. Root had been persistent in reaching out to the brothers and asking for permission to witness their tests. He was there the first time they flew their machine in a complete circle.

Amos Root wrote about this achievement in his beekeeping publication and sent a copy to the editor of Scientific American, who – you guessed it – ignored the news.

Lesson #5: Don’t be surprised when your breakthrough isn’t your breakthrough

Word was trickling out, but the key word here is trickling. There was some communication with the U.S. and French governments, and with private investors. But the brothers were still pretty much on their own, struggling to keep their endeavor moving forward.

Their tests continued to advance. Instead of flying, say, 1000 feet, the duration of their test flights rose to 11, 12 and then 15 miles.

Lesson #6: Tolerate failure, but avoid disaster

The brothers had one cardinal rule that served them well. They never flew together. In the event of a fatal crash, they did not want their program to die, too. If one of them survived, the initiative could still continue.

In 1906, Scientific American took notice and published a serious article about the brothers’ efforts. The patent they applied for in 1903 was also granted in 1906. The world started to take notice. Crowds gathered to watch their flights. The brothers had succeeded, but only because they kept going when the world was too preoccupied to recognize the wisdom and importance of their efforts.

Bonus lesson: test, test, test

The Wright brothers didn’t sit in an office and dream. They didn’t create a Powerpoint and pitch an unformed idea. They went out into the field (literally) and tested their prototypes, risking their lives in the process. Success eventually came because they built something of value that the world needed, even if the world didn’t recognize it yet.

Test your ideas. Prove your theories. Make people understand.


Sturdy Quadcopter Build

Sturdy Quadcopter Build


Comprehensive guide to build a simple quadcopter for beginners.
With skills like basic soldering and electronics, Chris Schroeder shows you step-by-step how to build from scratch a quadcopter. The guide is intended for beginner users having a plug-and-play construction system and a simple programming code.

All components are purchased from online stores while for programming the designer used a flight control board and a programming card. The values for the flying robot are set by the brushless Electronic Speed Controller (ESC).

Below is an impressive list of the main parts needed to build the quadcopter.



How to Fly Your Quadcopter Like a Pro: 7 Important Tips


Image Source: instructables

REMEMBER: You Will Discover 7 MOST Important Tips for Flying Your New Quadcopter or Drone! Number 4 Is Really Interesting! These Tips Helped Over 28,000 Readers!

Flying a quadcopter is much harder than it looks. While people love bragging and showing off their flying skills, new pilots often crash and burn a few times before learning how to really master their flying. The following tips will allow you to fly your quadcopter like a pro in no time.

1. Do Not Go to Manual Mode Too Fast

Manual mode is meant for expert flyers. When in manual mode, the systems put in place to help make flying easier will not provide the extra stability you need. This forces you to either be a great pilot or crash and burn in the process.

Manual mode, should by no means, be engaged unless you really know how to fly your copter. When you feel that it is time for manual mode, choose your practice location safely.

Learn how to fly at low altitudes at first until you understand manual mode, and then start flying higher.

2. Be Very Cautious of Windy Conditions

Wind is the downfall of most copters. If you notice that 10 – 20+ mile per hour winds are outside, you will not want to bring your copter out for flight.

There are some copters that have automatic correction for windy conditions and will adjust for the gusts of wind by altering the motor speeds accordingly.

As a general rule of thumb, you will also want to check the current mode setting of your copter. If the mode is set on indoors, you will want to switch it to outdoor mode for better overall stability and control.

3. Use GPS Mode if Available

More expensive models come with GPS mode. This is a mode that will use GPS to know where the copter is in space.

This is a great feature for precision flying or when you want to take video or images of a specific location and you really want to pinpoint the location on the map.

Furthermore, GPS mode provides great flight advantages that the beginner and advanced pilot will be able to take advantage of from their very first flight.

When in GPS mode, you will be able to take your hands off of the copter and it will balance itself and hover. This is ideal for pilots transitioning to be a pro. When you get nervous or you are unsure of what to do, GPS mode will correct your faults and allow you to take a deep breath before flight continuation.

GPS mode also provides the major benefit of knowing exactly where your copter is located. If a crash does occur, you will be able to find the wreckage much easier if GPS mode is active.

4. Fight Wind Gusts With Caution

You can fight wind gusts with caution. There are some higher end models that allow you to control the pitch of your copter so that you can negate the gusts of wind. This is done through what is called anegative pitch, but it is very advanced.

When wind is coming and you feel yourself losing control of the copter, you will want to fight the wind by pushing against it.

If wind is hitting the left side, you will want to attempt to fly into the wind to counteract the change in direction. The goal is to fight the wind if possible, but you must also know when to put an end to your flight.

As a rule of thumb, you don’t want your helicopter to be too far away from you in the event that wind blows it out of operating range. When possible, keep your helicopter close and land it if the wind is too powerful.

5. Keep Controls Simple

Up, down, left and right are the controls you want to master. Do not waste time trying to do rolls or advanced techniques until you have had months of flight experience. When you want to practice more advanced methods of flight, you should do so in optimal weather conditions. It is never a good idea to try doing a roll or flip for the first time when the weather is bad.

Keep all of your controls as simple as possible so that you can learn to fly the right way.

6. Master Hovering

Those that haven’t mastered flying will find that hovering is very difficult, but it is also very useful.

When you learn to hover, not only will you be able to take better pictures and videos, but you will be able to have full control over your copter.

A few tips on hovering are as follows:

  • Hoover 4 – 5 feet or higher in the air. When hovering too low, you can cause a disturbance from the force of the blades against the ground.
  • Maintain a proper throttle, pitch and roll to stay hovering in the same spot.

Hovering is very difficult and will take some time to master. Many models do not come with a pitch control. Instead, users will have the copter’s system control this part of flight.

7. Learn to Turn Off the Throttle

Crashing comes with the possibility of severely damaging your copter. When the copter crashes, you will want to learn to shut off the throttle as fast as possible.

This will stop the blades from rotating. When the throttle is turned off, further damage is prevented and there is less of a chance that the motors will suffer damage in the process.

While this may not seem like a pro tip, you must learn how to crash because it can and does happen quite a bit. Unfortunately, crashing will occur when you least expect it, so always ensure you are ready to cut the throttle in an instant.

As a pro pilot, you will also want to purchase propeller guards. These guards are small, easy to install and are ideal if a crash occurs. When the propellers are twirling, the guards will keep them from hitting the ground, trees or any other objects nearby.

Propeller guards will also provide you with further reaction time if the throttle is not cut fast or if the copter was pulled out of range by the wind before it crashed.


Working of Electric Motor

The electric motor is a device which converts electrical energy to mechanical energy. There are mainly three types of electric motor.

1) DC Motor

2) Induction Motor

3) Synchronous Motor.

All of these motors work in more or less same principle. Working of electric motor mainly depends upon the interaction of magnetic field with current. Now we will discuss the basic operating principle of electric motor one by one for better understanding the subject.


Image Source :

Working of DC Motor

Working principle of DC Motor mainly depends upon Fleming Left Hand rule. In a basic dc motor, an armature is placed in between magnetic poles. If the armature winding is supplied by an external dc source, current starts flowing through the armature conductors. As the conductors are carrying current inside a magnetic field, they will experience a force which tends to rotate the armature. Suppose armature conductors under N poles of the field magnet, are carrying current downwards (crosses) and those under S poles are carrying current upwards (dots). By applying Fleming’s Left hand Rule, the direction of force F, experienced by the conductor under N poles and the force experienced by the conductors under S poles can be determined. It is found that at any instant the forces experienced by the conductors are in such a direction that they tend to rotate the armature.

Again, due this rotation the conductors under N – poles come under S – pole and the conductors under S – poles come under N – pole. While the conductors go form N – poles to S – pole and S – poles to N – pole, the direction of current through them, is reversed by means of commutator. Due to this reversal of current, all the conductors come under N – poles carry current in downward direction and all the conductors come under S – poles carry current in upward direction as shown in the figure. Hence, every conductor comes under N – pole experiences force in same direction and same is true for the conductors come under S – poles. This phenomenon helps to develop continuous and unidirectional torque.

Working of DC Motor Video – Click Here

Working of Induction Motor

Working of electric motor in the case of induction motor is little bit different from dc motor. In single phase induction motor, when a single phase supply is given to the stator winding, a pulsating magnetic field is produced and in a three phase induction motor, when three phase supply is given to three phase stator winding, a rotating magnetic field is produced. The rotor of an induction motor is either wound type or squirrel cadge type. Whatever may be the type of rotor, the conductors on it are shorted at end to form closed loop. Due to rotating magnetic field, the flux passes through the air gap between rotor and stator, sweeps past the rotor surface and so cuts the rotor conductor. Hence according to Faraday’s law of electromagnetic induction, there would be a induced current circulating in the closed rotor conductors. The amount of induced current is proportional to the rate of change of flux linkage with respect to time. Again this rate of change of flux linkage is proportional to the relative speed between rotor and rotating magnetic field. As per Lenz law the rotor will try to reduce the every cause of producing current in it. Hence the rotor rotates and tries to achieve the speed of rotating magnetic field to reduce the relative speed between rotor and rotating magnetic field.

Working of Induction Motor Video – Click Here

Working of schronous Motoryn

In synchronous motor, when balanced three phase supply is given to the stationary three phase stator winding, a rotating magnetic field is produced which rotates at synchronous speed. Now if an electromagnet is placed inside this rotating magnetic field, it is magnetically locked with the rotating magnetic field and the former rotates with the rotating magnetic field at same speed that is at synchronous speed.

Working of Schronous Motor – Click Here






Multi-rotors are unique in the world of R/C hobbyists. Usually, when it comes to controlling a model boat or plane, the pilot has absolute, precise control over the motor. A nudge of the throttle translates to a proportional increase in RPM. The same is true of input to the rudders, ailerons, flaps, and other parts involved in changing speed or direction.

The distinction with multi-rotors, whether or not advantageous, is that no human is capable of controlling the rotational speeds of three or more motors simultaneously with enough precision to balance a craft in the air. This is where flight controllers come into play.

A flight controller (FC) is a small circuit board of varying complexity. Its function is to direct the RPM of each motor in response to input. A command from the pilot for the multi-rotor to move forward is fed into the flight controller, which determines how to manipulate the motors accordingly.

The majority of flight controllers also employ sensors to supplement their calculations. These range from simple gyroscopes for orientation to barometers for automatically holding altitudes. GPS can also be used for auto-pilot or fail-safe purposes. More on that shortly.

With a proper flight controller setup, a pilot’s control inputs should correspond exactly to the behavior of the craft. Flight controllers are configurable and programmable, allowing for adjustments based on varying multi-rotor configurations. Gains or PIDs are used to tune the controller, yielding snappy, locked-in response. Depending on your choice of flight controller, various software is available to write your own settings.

Many flight controllers allow for different flight modes, selectable using a transmitter switch. An example of a three-position setup might be a GPS lock mode, a self-leveling mode, and a manual mode. Different settings can be applied to each profile, achieving varying flight characteristics.

Getting To Know Flight Controllers

DJI, arguably the dominant player in multi-rotors, produces two models. The Naza-M Lite is a high-quality, easy-to-set up unit with GPS and fail-safe capacities. Its Naza-M V2 is virtually identical, but includes a handful of additional features, such as the ability to daisy chain DJI expansions (a Bluetooth module, for example). Also, it allows up to eight motors, rather than six.

              DJI Naza Lite flight controller

 DJI Naza Lite flight controller

Multiple flight modes are available: GPS lock, altitude lock, orientation mode (moving forward always happens away from take-off point, regardless of craft rotation), and a non-stabilized manual mode.

The Nazas are the ultimate hobby flight controllers, with a multitude of features, optimized ease of use, and relatively straightforward setup. They may, however, no be the best choice for every multi-rotor. Let’s get into why.



For many simulations of real world engineering applications, the predictions of heat transfer properties are as important, if not more important, than the actual flow field. Such scenarios include simulations of heat exchangers, HVAC (Heating, Ventilation and Air Conditioning), combustion/burners, electronics cooling, and many more. In these applications, we are often interested in how heat moves through both the fluid and solid domains, and importantly the transfer of heat across the interface between adjacent domains.

ANSYS CFD is a leader in solving all three modes of heat transfer: convection, conduction and radiation. Deciding which physics to include is critical to setting up an efficient CFD model. For instance, radiation provides a computational overhead but it is a very important heat transfer mode for bodies with high temperatures which radiate to cooler adjacent bodies or to a lower ambient temperature (since radiative heat transfer scales with Temperature4).

This image shows the heat that is convected away from a finned heat exchanger. As indicated by the streamlines, air is flowing from left to right in the image.


Conjugate Heat Transfer (CHT) is applicable whenever there are two adjacent domains and we wish to analyze the heat transfer between these domains. These domains can either be solid or fluid domains. One example is the forced or natural convective cooling of a heat-sink attached to active electronics components which generate heat.

As well as heat-transfer across solid-fluid domains, we can also resolve heat transfer across solid-solid domains and fluid-fluid domains. Solid-solid interfaces are used where two solid components are in contact with each other and there is heat flowing between the objects. Although a fluid-fluid CHT system may seem unphysical, it is a valid assumption in some cases, such as a co-flow heat-exchanger where two fluids are separated by a thin wall. In this case, it can be assumed that the heat-transfer across the dividing wall is calculated in the wall normal dimension only (without explicitly meshing the wall thickness), and there is negligible heat flow along the wall.

In all of the above instances, a thermal resistance can be applied to the interface in ANSYS CFD. Such resistances can be used to represent thermal coatings (often used in electronics applications) or badly mated surfaces between adjacent solids (to understand the tolerance of poorly designed connections).


This image shows a cross-section through the stream-normal plane of a finned heat exchanger. Heat is input to the system at the bottom boundary condition and is carried through the structure and out into the surrounding air.

For CHT simulations, it is critical to select appropriate boundary conditions that best represent the physical situation. ANSYS CFD provides a wide range of thermal boundary conditions, but also allows users to customise boundary conditions (using UDF’s or CCL Expressions) so that any heat transfer situation can be modeled.

One extremely important aspect of performing accurate CHT simulations is the wall adjacent mesh sizing, as accurately resolving the thermal boundary layer is crucial for producing reliable CHT results. To resolve the thermal boundary layer, an identical approach can used to when we are resolving the viscous boundary layer (for accurate flow separation, pressure drop, etc…), where we create high-aspect ratio prism or hexa elements stacked in the wall-normal direction (protruding into the fluid domain). Within the solid domain, however, there is no need to have such resolution (as there is no convection) so a uniform, coarser mesh can be used.

The use of Conjugate Heat Transfer simulation unlocks a range of simulations that can be performed using ANSYS CFD across industries including electronics, built environment and power generation. With proper training and knowledge, CHT simulations contribute an integral aspect of the Simulation-Driven Product Development approach that is being embraced by innovative designers and manufacturers worldwide. Contact LEAP today if you have an engineering problem where heat transfer is an issue.