Finite Element Analysis: Introduction
The following four-article series was published in a newsletter of the American Society of Mechanical Engineers (ASME). It serves as an introduction to the recent analysis discipline known as the finite element method. The author is an engineering consultant and expert witness specializing in finite element analysis.
Finite element analysis (FEA) is a fairly recent discipline crossing the boundaries of mathematics, physics, engineering and computer science. The method has wide application and enjoys extensive utilization in the structural, thermal and fluid analysis areas. The finite element method is comprised of three major phases: (1) pre-processing, in which the analyst develops a finite element mesh to divide the subject geometry into subdomains for mathematical analysis, and applies material properties and boundary conditions, (2) solution, during which the program derives the governing matrix equations from the model and solves for the primary quantities, and (3) post-processing, in which the analyst checks the validity of the solution, examines the values of primary quantities (such as displacements and stresses), and derives and examines additional quantities (such as specialized stresses and error indicators).
The advantages of FEA are numerous and important. A new design concept may be modeled to determine its real world behavior under various load environments, and may therefore be refined prior to the creation of drawings, when few dollars have been committed and changes are inexpensive. Once a detailed CAD model has been developed, FEA can analyze the design in detail, saving time and money by reducing the number of prototypes required. An existing product which is experiencing a field problem, or is simply being improved, can be analyzed to speed an engineering change and reduce its cost. In addition, FEA can be performed on increasingly affordable computer workstations and personal computers, and professional assistance is available.
It is also important to recognize the limitations of FEA. Commercial software packages and the required hardware, which have seen substantial price reductions, still require a significant investment. The method can reduce product testing, but cannot totally replace it. Probably most important, an inexperienced user can deliver incorrect answers, upon which expensive decisions will be based. FEA is a demanding tool, in that the analyst must be proficient not only in elasticity or fluids, but also in mathematics, computer science, and especially the finite element method itself.
Which FEA package to use is a subject that cannot possibly be covered in this short discussion, and the choice involves personal preferences as well as package functionality. Where to run the package depends on the type of analyses being performed. A typical finite element solution requires a fast, modern disk subsystem for acceptable performance. Memory requirements are of course dependent on the code, but in the interest of performance, the more the better, with 512 Mbytes to 8 Gbytes per user a representative range. Processing power is the final link in the performance chain, with clock speed, cache, pipelining and multi-processing all contributing to the bottom line. These analyses can run for hours on the fastest systems, so computing power is of the essence.
One aspect often overlooked when entering the finite element area is education. Without adequate training on the finite element method and the specific FEA package, a new user will not be productive in a reasonable amount of time, and may in fact fail miserably. Expect to dedicate one to two weeks up front, and another one to two weeks over the first year, to either classroom or self-help education. It is also important that the user have a basic understanding of the computer’s operating system.
Incoming search terms:
Trainings To Up Grade The Quality
In the era where the number of labors is much bigger than the working places has result the high figure of unemployment. Working places for a higher level of education and lower education background are all the same, it is so limited that could not enough employ the human resources. It is a pity to see the many potential people who graduated from the high level of education but still they do not have the chance to work. Moreover if the people are in the level of lower education and not having any plus skills they will positively be unemployed.
To add more skills people can go to a training center where skills from many kinds of filed are able to be trained. Technology is progressing with no tolerance; every month new technologies are invented. This will make training will help people to catch the tack. With joining an IT Training will help one to be updated with the Information and Technology.
Training can be held with group or individual. This training of IT will stock the knowledge of software, server system, multimedia, business intelligence, and many more. The company, who is interested in up grading the knowledge of its employee, is also able to order the trainer to make seminar in the company.
Categories: Uncategorized Tags: business intelligence, l
Artificial Intelligence And Intuition
The intuitive algorithm
Roger Penrose considered it impossible. Thinking could never imitate a computer process. He said as much in his book, The Emperor’s New Mind. But, a new book, The Intuitive Algorithm, (IA), suggested that intuition was a pattern recognition process. Intuition propelled information through many neural regions like a lightning streak. Data moved from input to output in a reported 20 milliseconds. The mind saw, recognized, interpreted and acted. In the blink of an eye. Myriad processes converted light, sound, touch and smell instantly into your nerve impulses. A dedicated region recognized those impulses as objects and events. The limbic system, another region, interpreted those events to generate emotions. A fourth region responded to those emotions with actions. The mind perceived, identified, evaluated and acted. Intuition got you off the hot stove in a fraction of a second. And it could be using a simple algorithm.
Is instant holistic evaluation impossible?
The system, with over a hundred billion neurons, processed the information from input to output in just half a second. All your knowledge was evaluated. Walter Freeman, the famous neurobiologist, defined this amazing ability. “The cognitive guys think it’s just impossible to keep throwing everything you’ve got into the computation every time. But, that is exactly what the brain does. Consciousness is about bringing your entire history to bear on your next step, your next breath, your next moment.” The mind was holistic. It evaluated all its knowledge for the next activity. How could so much information be processed so quickly? Where could such knowledge be stored?
Exponential growth of the search path
Unfortunately, the recognition of subtle patterns posed formidable problems for computers. The difficulty was an exponential growth of the recognition search path. The problems in the diagnosis of diseases was typical. Normally, many shared symptoms were presented by a multitude of diseases. For example, pain, or fever could be indicated for many diseases. Each symptom pointed to several diseases. The problem was to recognize a single pattern among many overlapping patterns. When searching for the target disease, the first selected ailment with the first presented symptom could lack the second symptom. This meant back and forth searches, which expanded exponentially as the database of diseases increased in size. That made the process absurdly long drawn – theoretically, even years of search, for extensive databases. So, in spite of their incredible speed, rapid pattern recognition on computers could never be imagined.
The Intuitive Algorithm
But, industry strength pattern recognition was feasible. IA introduced an algorithm, which could instantly recognize patterns in extended databases. The relationship of each member of the whole database was coded for each question.
(Is pain a symptom of the disease?)
Disease1Y, Disease2N, Disease3Y, Disease 4Y, Disease5N, Disease6N, Disease7Y, Disease8N, Disease9N, Disease10N, Disease11Y, Disease12Y, Disease13N, Disease14U, Disease15Y, Disease16N, Disease17Y, Disease18N, Disease19N, Disease20N, Disease21N, Disease22Y, Disease23N, Disease24N, Disease25U, Disease26N, Disease27N, Disease28U, Disease27Y, Disease30N, Disease31U, Disease32Y, Disease33Y, Disease34U, Disease35N, Disease36U, Disease37Y, Disease38Y, Disease39U, Disease40Y, Disease41Y, Disease42U, Disease43N, Disease44U, Disease45Y, Disease46N, Disease47N, Disease48Y,
(Y = Yes: N = No: U = Uncertain)
The key was to use elimination to evaluate the database, not selection. Every member of the database was individually coded for elimination in the context of each answer.
(Is pain a symptom of the disease? Answer: YES)
Disease1Y, xxxxxxN, Disease3Y, Disease4Y, xxxxxx5N, xxxxxx6N, Disease7Y, xxxxxx8N, xxxxxx9N, xxxxxx0N, Disease11Y, Disease12Y, xxxxxx13N, Disease14U, Disease15Y, xxxxxx16N, Disease17Y, xxxxxx18N, xxxxxx19N, xxxxxx20N, xxxxxx21N, Disease22Y, xxxxxx23N, xxxxxx24N, Disease25U, xxxxxx26N, xxxxxx27N, Disease28U, Disease27Y, xxxxxx30N, Disease31U, Disease32Y, Disease33Y, Disease34U, xxxxxx35N, Disease36U, Disease37Y, Disease38Y, Disease39U, Disease40Y, Disease41Y, Disease42U, xxxxxx43N, Disease 44U, Disease45Y, xxxxxx46N, xxxxxx47N, Disease 48Y,
(All “N” Diseases eliminated.)
For disease recognition, if an answer indicated a symptom, IA eliminated all diseases devoid of the symptom. Every answer eliminated, narrowing the search to reach diagnosis.
(Is pain a symptom of the disease? Answer: NO)
xxxxxx1Y, Disease2N, xxxxxx3Y, xxxxxx4Y, Disease5N, Disease6N, xxxxxx7Y, Disease8N, Disease9N, Disease10N, xxxxxx11Y, xxxxx12Y, Disease13N, Disease14U, xxxxxx15Y, Disease16N, xxxxxx17Y, Disease18N, Disease19N, Disease20N, Disease21N, xxxxxx22Y, Disease23N, Disease24N, Disease25U, Disease26N, Disease27N, Disease28U, xxxxxx27Y, Disease30N, Disease31U, xxxxxx32Y, xxxxxx33Y, Disease34U, Disease35N, Disease36U, xxxxxx37Y, xxxxxx38Y, Disease39U, xxxxxx40Y, xxxxxx41Y, Disease42U, Disease43N, Disease 44U, xxxxxx45Y, Disease46N, Disease47N, xxxxxx48Y,
(All “Y” Diseases eliminated.)
If the symptom was absent, IA eliminated all diseases which always exhibited the symptom. Diseases, which randomly presented the symptom were retained in both cases. So the process handled uncertainty – the “Maybe” answer, which normal computer programs could not handle.
(A sequence of questions narrows down to Disease29 – the answer.)
xxxxxx1Y, xxxxxx2N, xxxxxx3Y, xxxxxx4Y, xxxxxx5N, xxxxxx6N, xxxxxx7Y, xxxxxx8N, xxxxxx9N, xxxxxx10N, xxxxxx11Y, xxxxxx12Y, xxxxxx13N, xxxxxx14U, xxxxxx15Y, xxxxxx16N, xxxxxx17Y,xxxxxx18N, xxxxxx19N, xxxxxx20N, xxxxxx21N, xxxxxx22Y, xxxxxx23N, xxxxxx24N, xxxxxx25U, xxxxxx26N, xxxxxx27N, xxxxxx28U, Disease29Y, xxxxxx30N, xxxxxx31U, xxxxxx32Y, xxxxxx33Y, xxxxxx34U, xxxxxx35N, xxxxxx36U, xxxxxx37Y, xxxxxx38Y, xxxxxx39U, xxxxxx40Y, xxxxxx41Y, xxxxxx42U, xxxxxx43N, xxxxxx44U, xxxxxx45Y, xxxxxx46N, xxxxxx47N, xxxxxx48Y.
(If all diseases are eliminated, the disease is unknown.)
Instant pattern recognition
IA was proved in practice. It had powered Expert Systems acting with the speed of a simple recalculation on a spreadsheet, to recognize a disease, identify a case law or diagnose the problems of a complex machine. It was instant, holistic, and logical. If several parallel answers could be presented, as in the multiple parameters of a power plant, recognition was instant. For the mind, where millions of parameters were simultaneously presented, real time pattern recognition was practical. And elimination was the key.
Elimination = Switching off
Elimination was switching off – inhibition. Nerve cells were known to extensively inhibit the activities of other cells to highlight context. With access to millions of sensory inputs, the nervous system instantly inhibited – eliminated trillions of combinations to zero in on the right pattern. The process stoutly used “No” answers. If a patient did not have pain, thousands of possible diseases could be ignored. If a patient could just walk into the surgery, a doctor could overlook a wide range of illnesses. But, how could this process of elimination be applied to nerve cells? Where could the wealth of knowledge be stored?
Combinatorial coding
The mind received kaleidoscopic combinations of millions of sensations. Of these, smells were reported to be recognized through a combinatorial coding process, where nerve cells recognized combinations. If a nerve cell had dendritic inputs, identified as A, B, C and so on to Z, it could then fire, when it received inputs at ABC, or DEF. It recognized those combinations. The cell could identify ABC and not ABD. It would be inhibited for ABD. This recognition process was recently reported by science for olfactory neurons. In the experiment scientists reported that even slight changes in chemical structure activated different combinations of receptors. Thus, octanol smelled like oranges, but the similar compound octanoic acid smelled like sweat. A Nobel Prize acknowledged that discovery in 2004.
Galactic nerve cell memories
Combinatorial codes were extensively used by nature. The four “letters” in the genetic code – A, C, G and T – were used in combinations for the creation of a nearly infinite number of genetic sequences. IA discusses the deeper implications of this coding discovery. Animals could differentiate between millions of smells. Dogs could quickly sniff a few footprints of a person and determine accurately which way the person was walking. The animal’s nose could detect the relative odour strength difference between footprints only a few feet apart, to determine the direction of a trail. Smell was identified through remembered combinations. If a nerve cell had just 26 inputs from A to Z, it could receive millions of possible combinations of inputs. The average neuron had thousands of inputs. For IA, millions of nerve cells could give the mind galactic memories for combinations, enabling it to recognize subtle patterns in the environment. Each cell could be a single member of a database, eliminating itself (becoming inhibited) for unrecognized combinations of inputs.
Elimination the key
Elimination was the special key, which evaluated vast combinatorial memories. Medical texts reported that the mind had a hierarchy of intelligences, which performed dedicated tasks. For example, there was an association region, which recognized a pair of scissors using the context of its feel. If you injured this region, you could still feel the scissors with your eyes closed, but you would not recognize it as scissors. You still felt the context, but you would not recognize the object. So, intuition could enable nerve cells in association regions to use perception to recognize objects. Medical research reported many such recognition regions.
Serial processing
A pattern recognition algorithm, intuition enabled the finite intelligences in the minds of living things to respond holistically within the 20 millisecond time span. These intelligences acted serially. The first intelligence converted the kaleidoscopic combinations of sensory perceptions from the environment into nerve impulses. The second intelligence recognized these impulses as objects and events. The third intelligence translated the recognized events into feelings. A fourth translated feelings into intelligent drives. Fear triggered an escape drive. A deer bounded away. A bird took flight. A fish swam off. While the activities of running, flying and swimming differed, they achieved the same objective of escaping. Inherited nerve cell memories powered those drives in context.
The mind – seamless pattern recognition
Half a second for a 100 billion nerve cells to use context to eliminate irrelevance and deliver motor output. The time between the shadow and the scream. So, from input to output, the mind was a seamless pattern recognition machine, powered by the key secret of intuition – contextual elimination, from massive acquired and inherited combinatorial memories in nerve cells.
