You Must Be Aware Of This Brief History

Submitted by: Allan GKG

Finite Element Analysis (FEA) was first developed in 1943 by R. Courant, who utilized the Ritz method of numerical analysis and minimization of variation calculus to obtain approximate solutions to vibration systems. Courant’s contribution was evolutionary; drawing on a large body of earlier results for PDEs (partial differential equations) developed by Rayleigh, Ritz and Gale kin. Shortly thereafter, a paper published in 1956 by M. J. Turner, R. W. Clough, H. C. Martin, and L. J. Top established a broader definition of numerical analysis. The paper centered on the “stiffness and deflection of complex structures” . Development of the method began in earnest in the middle to late 1950s for airframe and structural analysis, and picked up a lot of steam at Berkeley in the 1960s for use in civil engineering.

By the early 70’s, FEA was limited to expensive mainframe computers generally owned by the aeronautics, automotive, defense, and nuclear industries. In 1970s, the finite element methods were developed rapidly with the development of the computer technologies. The research areas of finite element methods from then on are mostly involved in the mathematical and mechanical theory fundamentals, element construction, shape functions, numerical methods and their errors and convergence, programming and software technologies, and engineering applications in many fields, FEA has been developed to an incredible precision. Present day supercomputers are now able to produce accurate results for all kinds of parameters. The Basic Theory

The most efficient method of learning is by example. Therefore, we would like to present to you a simple FEA problem: the case of a three-member truss. The method of solution to this problem should demonstrate the basic concepts of FEA which are present in any analysis.

Before introducing specific quantities for our example, let’s first take a look at our structure as Fig. The overall objective of our analysis will be to determine the displacements of the truss members given the load P. This application of FEA to a simple three- member truss shows in general how the method works. Most applications to engineering problems, however, are much more complex. Such analyses require large numbers of elements and nodes in order to accurately represent the physical system being studied. These analyses inevitably require the application of a computer.

Welcome to Home of quality replica watches – Watchescat.com. As both retailer and wholesaler, Watchescat.com specializes in exporting replica watches. Prominent manufacturers are resources of Watchescat.com. With an eye to providing customers the highest quality products, Watchescat.com only accepts products from famous manufacturers that meeting the strictest standards. To ensure each customer a satisfied product, our whole business process is monitored and inspected by our teammates from manufacturing to packaging.Finite Element Analysis (FEA) was first developed in 1943 by R. Courant, who utilized the Ritz method of numerical analysis and minimization of variation calculus to obtain approximate solutions to vibration systems. Courant’s contribution was evolutionary; drawing on a large body of earlier results for PDEs (partial differential equations) developed by Rayleigh, Ritz and Gale kin. Shortly thereafter, a paper published in 1956 by M. J. Turner, R. W. Clough, H. C. Martin, and L. J. Top established a broader definition of numerical analysis. The paper centered on the “stiffness and deflection of complex structures” . Development of the method began in earnest in the middle to late 1950s for airframe and structural analysis, and picked up a lot of steam at Berkeley in the 1960s for use in civil engineering.

By the early 70’s, FEA was limited to expensive mainframe computers generally owned by the aeronautics, automotive, defense, and nuclear industries. In 1970s, the finite element methods were developed rapidly with the development of the computer technologies. The research areas of finite element methods from then on are mostly involved in the mathematical and mechanical theory fundamentals, element construction, shape functions, numerical methods and their errors and convergence, programming and software technologies, and engineering applications in many fields, FEA has been developed to an incredible precision. Present day supercomputers are now able to produce accurate results for all kinds of parameters. The Basic Theory

The most efficient method of learning is by example. Therefore, we would like to present to you a simple FEA problem: the case of a three-member truss. The method of solution to this problem should demonstrate the basic concepts of FEA which are present in any analysis.

Before introducing specific quantities for our example, let’s first take a look at our structure as Fig. The overall objective of our analysis will be to determine the displacements of the truss members given the load P. This application of FEA to a simple three- member truss shows in general how the method works. Most applications to engineering problems, however, are much more complex. Such analyses require large numbers of elements and nodes in order to accurately represent the physical system being studied. These analyses inevitably require the application of a computer.

Welcome to Home of quality replica watches – Watchescat.com. As both retailer and wholesaler, Watchescat.com specializes in exporting replica watches. Prominent manufacturers are resources of Watchescat.com. With an eye to providing customers the highest quality products, Watchescat.com only accepts products from famous manufacturers that meeting the strictest standards. To ensure each customer a satisfied product, our whole business process is monitored and inspected by our teammates from manufacturing to packaging.

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