Archive for August 2013
Delaunay triangulation method of unstructured mesh generation
Delaunay Triangulation
In mathematics and computational geometry, a Delaunay triangulation for a set P of points in a plane is a triangulation DT(P) such that no point in P is inside the circumcircle of any triangle in DT(P). Delaunay triangulation maximize the minimum angle of all the angles of the triangles in the triangulation; they tend to avoid skinny triangles. For a set of points on the same line there is no Delaunay triangulation (the notion of triangulation is degenerate for this case). For four or more points on the same circle (e.g., the vertices of a rectangle) the Delaunay triangulation is not unique: each of the two possible triangulations that split the quadrangle into two triangles satisfies the "Delaunay condition", i.e., the requirement that the circumcircles of all triangles have empty interiors.
Voronoi Diagram (The dual of delaunay triangulation)
In mathematics, a Voronoi diagram is a way of dividing space into a number of regions. A set of points (called seeds, sites, or generators) is specified beforehand and for each seed there will be a corresponding region consisting of all points closer to that seed than to any other. The regions are called Voronoi cells. In the simplest and most familiar case (shown in the first picture), we are given a finite set of points {p1,...,pn} in the Euclidean plane. In this case each site pk is simply a point and its corresponding Voronoi cell (also called Voronoi region or Dirichlet cell) Rk consisting of every point whose distance to pk is less than or equal to its distance to any other site. Each such cell is obtained from the intersection of half-spaces, and hence it is a convex polygon. The segments of the Voronoi diagram are all the points in the plane that are equidistant to the two nearest sites. The Voronoi vertices (nodes) are the points equidistant to three (or more) sites.
Introduction to meshing
Connectivity based classification of meshes:
- Structured Meshes: A structured mesh is characterized by regular connectivity that can be expressed as a two or three dimensional array. This restricts the element choices to quadrilaterals in 2D or hexahedra in 3D. The above example mesh is a structured mesh, as we could store the mesh connectivity in a 40 by 12 array. The regularity of the connectivity allows us to conserve space since neighborhood relationships are defined by the storage arrangement. Additional classification can be made upon whether the mesh is conformal or not.
The simplest algorithms directly compute nodal placement from some given function. These algorithms are referred to as algebraic algorithms. Many of the algorithms for the generation of structured meshes are descendants of "numerical grid generation" algoritms, in which a differential equation is solved to determine the nodal placement of the grid. In many cases, the system solved is an elliptic system, so these methods are often referred to as elliptic methods. - Unstructured Mesh : An unstructured mesh is characterized by irregular connectivity is not readily expressed as a two or three dimensional array in computer memory. This allows for any possible element that a solver might be able to use. Compared to structured meshes, the storage requirements for an unstructured mesh can be substantially larger since the neighborhood connectivity must be explicitly stored.
It is difficult make general statements about unstructured mesh generation algorithms because the most prominent methods are very different in nature. The most popular family of algorithms are those based upon Delaunay triangulation, but other methods, such as quadtree/octree approaches are also used.
Why the "meshed up" name??
This post will not only give a reason for the meshed up name, but also the beginning of my current topic of study, Finite Element Analysis (FEA).
Finite element analysis is a numerical technique for finding approximate solutions of boundry value problems. This method involves dividing the domain of the problem into a collection of subdomains, with each subdomain represented by a set of element equations to the original problem, followed by systematically recombining all sets of element equations into a global system of equations for the final calculation. The global system of equations has known solution techniques, and can be calculated from the initial values of the original problem to obtain a numerical answer.
(^^ a hell of an introduction .. wasn't it?? :P)
In simple words in finite element analysis is a method of solving a bunch of complicated equations over a large area(domain) by dividing it into small parts(sub domains) and solving the generalized equations for each part and then combining their individual solutions to give the combined solution for the whole area. It is mainly used in analysis of complex geometries where the subdomains are not symmetrical.
And the division of the domain is done by generating a mesh over the area thus dividing it into subdomains.
(^^ a hell of an introduction .. wasn't it?? :P)
In simple words in finite element analysis is a method of solving a bunch of complicated equations over a large area(domain) by dividing it into small parts(sub domains) and solving the generalized equations for each part and then combining their individual solutions to give the combined solution for the whole area. It is mainly used in analysis of complex geometries where the subdomains are not symmetrical.
And the division of the domain is done by generating a mesh over the area thus dividing it into subdomains.
The meshing done on an airframe dividing it into small parts. The more complicated the object the finer the mesh is.
Symmentrical Meshing over a cube. the solution over each part, of each face will be the same.
The New One: Aarush-M
Aarush-M is the smaller version of Aarush-X1, was designed by the team for participation in AUVSI SUAS '13, the annual student unmanned aerial system competition held annually in Maryland,USA. Aarush-M is a twin-boom, inverted V-tail UAS designed for delivering situational awareness in a disaster struck area. Command and control over UAS is done via a 2.4 GHz radio link, while the intelligence gathered is transmitted over a 5 GHz link. A highly modular and portable system, Aarush-M can be flight ready in less than 30 minutes, providing an endurance of 20 minutes.
Aarush-M is a twin boom inverted v-tail pusher aircraft with a wingspan of 122” and having an empty weight of 32 lbs.. The airframe has been designed and fabricated by undergraduate mechanical engineering students of the team. It is powered by Hacker A80-8 electric motor with a 22x8 propeller. A single axis gimbal for the camera has been integrated with the system, to provide +/- 45 degree roll compensation.
One of the ancillary objectives of the team was to develop a robust aerial platform fit for indigenous research, besides performing in SUAS ‘13. The fabrication process for the new airframe was carried out completely in the UAS-DTU lab at DTU. The fuselage features a monocoque shell design composed of carbon fiber/epoxy sandwiching balsa sheet for additional stiffness. Sandwiched laminates of carbon fiber, glass fiber and balsa sheet were made for testing and experimentally determining their strengths which would be further used for wing and tail skins. As a result 200 GSM glass fiber (45 degrees) and balsa sheet were used. The design features twin CF booms and solid spring CF landing gear. Landing gear, wing & tail skins were manufactured using CNC cut medium density fiber molds. The wing assembly consists of two outboard sections and one mid-section.
Aarush-M was indigenously fabricated over a period of 3 months followed by 5 weeks of rigorous flight testing making the UAS flight ready for the competition.
Suas '13 was held from 19-22 June 2013 where 35 teams competed. Aarush-M bagged the team 6th position in the competition.
Aarush-X1 : The next generation UAV
Aarush-X1 is the result of an industry-academia collaboration between Lockheed Martin and
Delhi Technological University. The Unmanned Aerial System has been designed and fabricated by a group of undergraduate students of the university, who received timely guidance from mentors in the faculty and Lockheed Martin. The UAS has been designed according to the
constraints imposed by urban environments, making the system invaluable for ISR in cities like
Delhi and Mumbai. The system, in fact, can be modified to adapt to specific mission-dependent requirements.
The UAS was unveiled by Dr. V.K.Saraswat, Director General, D.R.D.O, on November 2nd,
2012, at the Lokarpan Ceremony held at the India Habitat Center. The ceremony was presided
over by Dr. D.N. Reddy (title), and Dr.R.P.Aggarwal. The event witnessed a small presentation
by the student project manger and team captain, outlining the design and fabrication process
adopted by the team. Mr. John Sheehan, who along with Dr. Peter Drewes, mentored the students, highlighted the key accomplishments of the project, and congratulated the students on their achievement. Mr. Abhay Paranjape, (title) also attended the ceremony and emphasized on the importance of the sustenance of student effort, and long term relationships between industry and academia , in his talk.
Dr. V.K.Saraswat lauded the student effort and expressed a desire to nurture the student talent. He also outlined some major capabilities that are demanded of current Unmanned Air Systems, like stealth and payload compatibility.The Lokarpan Ceremony was also attended by representatives
from HAL, NTRO, Army, IAF and DST.
Team UAS-DTU at public flight of Aarush-X1
The ceremony concluded with an invitation to all the attendees to witness the First Public Flight
of Aarush-X1, which was to be held the following day (November 3rd) at Karnal Institute of
Civil Aviation, Haryana.
The Flight Day was attended by engineers from HAL and NTRO amongst others.
The UAS did a single sortie for about 3 minutes. Telemetry and real time video, were displayed
at the portable ground station. The UAS was taxied to the viewing area, after the landing, for a
visual inspection by the attendees, which was followed by a question and answer session.
Team UAS-DTU with Lockheed Martin representatives Mr. John Sheehan and Dr Peter Drewes
From recruitment to the beginning of 2nd year (a summary of what i did)
October '12 :
My work in the team started with the lokarpan ceremony and public flight of Aarush X1, the next generation urban UAV built by the senior students in my team. Even though i didn't build the it, yet its worth posting a picture of it....
The real work started in December when the conceptual design of "the new one" began for SUAS '13. it was a month full of YouTube videos and tutorials trying to learn solidworks to make the CAD model for the new plane. After spending hours on my laptop this was the final result
January '13- March '13 :
May '13: Bad times yet again, exams!!!
June '13- July '13: As the team flew off to Maryland, USA for the competition. The summer break was spent on learning about Finite Element Analysis (FEA). All the time was spent in learning the basics of FEA along with simple problems on CFD and static structural analysis using ansys 14.
A bump in the road during the summers delayed the publishing of this blog however my main target would be to constantly update my success's , failure's, problems faced and their solutions which come up during my work leading up to designing of the next aircraft we make.
Thanks for reading!!
My work in the team started with the lokarpan ceremony and public flight of Aarush X1, the next generation urban UAV built by the senior students in my team. Even though i didn't build the it, yet its worth posting a picture of it....
Aarush X1 at Karnal Airport
November '12 : End Semester Examinations!!!!! huh bad times... :P
December '12 :The real work started in December when the conceptual design of "the new one" began for SUAS '13. it was a month full of YouTube videos and tutorials trying to learn solidworks to make the CAD model for the new plane. After spending hours on my laptop this was the final result
CAD model of Aarush-M
The model we designed was just a smaller version of aarush X1. We wanted to bring our innovative inverted v-tail design of Aarush X1 to the competition but since the competition has a size and weight limit for the competing aircraft's hence the smaller, similar aircraft with the similar name, Aarush-M was built.
These three months were the most tiring and hectic months of my life. The fabrication of Aarush-M was completely indigenous. These three months were the introduction to various composite construction techniques involving glass fiber and carbon fiber. Techniques like wet layup vacuum bagging and vacuum infusion were used in making the fuselage, wing and tail skins and the landing gear. Various mould making techniques like fiber glass moulding, router cut MDF moulding. The main aim during the fabrication was to reduce the weight of the plane as compared to its predecessor. This was followed by integration of the avionics with the airframe the make the complete UAS.
Fuselage Plug
Fiber Glass Moulding Of the Fuselage Plug
Fuselage Mould
The Carbon Fibre Fuselage Body
Internal Structure Of the Left Wing
Completed Left wing
31st March 2013- The First Flight!!!
Aarush-M at Bhiwani Airport
April '13:
The tedious days of flight testing. Preparing for Suas '13.June '13- July '13: As the team flew off to Maryland, USA for the competition. The summer break was spent on learning about Finite Element Analysis (FEA). All the time was spent in learning the basics of FEA along with simple problems on CFD and static structural analysis using ansys 14.
A bump in the road during the summers delayed the publishing of this blog however my main target would be to constantly update my success's , failure's, problems faced and their solutions which come up during my work leading up to designing of the next aircraft we make.
Thanks for reading!!
tHe NoOb POst (Who Am I??)
Howdy future followers,
as the heading suggests this is my first blog post ever so i guess its introduction time!!
HI!,
I am Ankit Saxena, currently living in New Delhi, India, pursuing B.Tech in Automobile Engineering from Delhi Technological University. I was Born and raised in the city of Nawab's, Lucknow.
"The first and simplest emotion which we discover in the human mind, is curiosity."
One of my favorite quotes ever. I try to follow it as much as i can, keeps my learning curve going up always and also makes me capable about blabbing all the time about random stuff which people really don't care about, The blabbing helps me sort people out. The people who at least pretend to care about my jibber-jabber are the one's who care. :P
Hobbies and Interests: mmmm... music, reading, movies, video games. Well everyone is into these now a days.
What i do that others usually don't : Collecting coins, a decent collection of old Indian coins along with some old foreign coins too!! (Now that's interesting :P).... Cooking, Not just maggi and omelette, a lot of other stuff too, specially non veg. I love both eating and cooking.
Now the professional side:
I am currently a member of UAS DTU, An undergraduate student tech team of my college which is involved in development of Unmanned Aerial Systems. I am in the airframes department of the team involved in Computer Aided Design (CAD) and Finite Element Analysis (FEA) along with indigenous fabrication of the airframes of the UAS's we build.
Now the professional side:
I am currently a member of UAS DTU, An undergraduate student tech team of my college which is involved in development of Unmanned Aerial Systems. I am in the airframes department of the team involved in Computer Aided Design (CAD) and Finite Element Analysis (FEA) along with indigenous fabrication of the airframes of the UAS's we build.
whats CAD and FEA you ask??
well this blog will be a journal of my activities related to my work in the field of FEA primarily helping me to maintain a log of all the effort i'm going to put in..
"It's not a silly question if you can't answer it"
well this blog will be a journal of my activities related to my work in the field of FEA primarily helping me to maintain a log of all the effort i'm going to put in..
"It's not a silly question if you can't answer it"
Another quote i'd like to follow so all questions and comments will always be welcomed...
Thanks!!
