Symbolic computation in structural engineering

Pavlović, M.N.

doi:10.1016/s0045-7949(03)00286-4

Cited by 36 publications

(21 citation statements)

References 77 publications

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“…Applications of symbolic computation, most commonly used at present through MATLAB [2], Maple [3], and Mathematica [4] were demonstrated in all major branches of engineering, ranging from electromagnetic waves [5] to structural engineering [6].…”

Section: Introductionmentioning

confidence: 99%

“…Among the advantages of exposing engineering students to symbolic computation is the opportunity for students and engineers to spend more time on modeling and interpreting results, and less time on technical aspects of solving algebraic problems [8]. The availability of symbolic computation also allows areas of classical analysis to "re-emerge as attractive computational options" [6], providing "a more balanced view that no longer sees analytical techniques and numerical methods as incompatible opposites but combines their usage in a rational way. "…”

Section: Introductionmentioning

confidence: 99%

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Symbolic Scientific Software Skills for Engineering Students

Abichandani

Primerano

Kam

2010

2010 IEEE Transforming Engineering Education: Creating Interdisciplinary Skills for Complex Global Environments

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Abstract-The emergence of powerful numeric and symbolic scientific software applications, including MATLAB, Maple, and Mathematica, has revolutionized engineering design. These applications have allowed users to perform computations and calculations at levels of sophistication and depth that were not available to practitioners even one generation ago. They have also given educators the ability to convey advanced mathematical and engineering concepts in new ways and spend more time on analysis of engineering systems and less time on remedial mathematics. This new capability, which has become a fundamental tool for sophisticated designers in industry, is still not fully embraced in many engineering curricula.To exemplify the potential of scientific software in the engineering classroom, we describe a laboratory exercise conducted by second-year engineering students at Drexel University. It introduces a geosynchronous satellite orbital entry problem, and demonstrates how scientific software can help students understand the behavior of an interesting physical system in a way that would have required much more effort using traditional methods.We believe that early introduction to symbolic computation tools and scientific software would be very valuable to engineering students. Such tools should become standard instruments in the arsenal of present-day engineers. Moreover, their use should be adopted across the curriculum (not only in introductory mathematics classes) and become part of the design experience in all engineering disciplines.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Symbolic Scientific Software Skills for Engineering Students

Abichandani

Primerano

Kam

2010

2010 IEEE Transforming Engineering Education: Creating Interdisciplinary Skills for Complex Global Environments

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“…Also, Pavlovi [21] presented an extensive compilation on symbolic analysis of some structural engineering areas. Fields such as finite elements and variational techniques are treated using symbolic manipulation.…”

Section: Introductionmentioning

confidence: 99%

Exact integration of the stiffness matrix of an 8‐node plane elastic finite element by symbolic computation

Videla

Baloa

Griffiths

et al. 2007

Numerical Methods Partial

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Computer algebra systems (CAS) are powerful tools for obtaining analytical expressions for many engineering applications in both academic and industrial environments.CAS have been used in this paper to generate exact expressions for the stiffness matrix of an 8-node plane elastic finite element. The Maple software system was used to identify six basic formulas from which all the terms of the stiffness matrix could be obtained. The formulas are functions of the Cartesian coordinates of the corner nodes of the element, and elastic parameters Young's modulus and Poisson's ratio.Many algebraic manipulations were performed on the formulas to optimize their efficiency. The redaction in CPU time using the exact expressions as opposed to the classical Gauss-Legendre numerical integration approach was over 50%. In an additional study of accuracy, it was shown that the numerical approach could lead to quite significant errors as compared with the exact approach, especially as element distortion was increased.

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“…The application of symbolic solvers has had a dramatic, positive impact on science and technology with various accounts of its effectiveness and application available 5,6,7,8 and its usage in education as a primary or complementary portion to enhance student understanding of concepts 9,10,11,12 . These solvers lend themselves exceptionally well to classical analysis of engineering problems.…”

Section: Use Of Symbolic Solversmentioning

confidence: 99%

Using Finite Element Methods to Calculate the Deflection of an Orifice Plate Subject to Uniform Pressure Distribution

Narendranath¹,

Deshpande²,

Kolati³

et al.

2016 ASEE Annual Conference &Amp; Exposition Proceedings

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Michigan Technological University with a Report option. His report was on the computational study of a non-cylindrical, non-comformable CNG tank mounting on a pickup truck frame using finite element methods. He is currently serving as a Graduate Teaching Assistant under Dr. Aneet Narendranath for a senior level introductory finite element method course. The major duties as an assistant involve guiding senior students in gaining computational knowledge of the applications of the finite element methods in solving simple engineering problems. Using Finite Element Methods to Calculate the deflection of an orifice plate subject to uniform pressure distribution Mr AbstractAs part of an elective course in Finite Element Methods (FEM) for senior level and graduate students in mechanical engineering, an ASME standard for flow measurement devices is used to design an orifice plate. Students are given a certain set of flow condition and equipment constraints that they must adhere to. As part of the design process, they are required to evaluate their orifice plate for strength via finite element methods and determine if the plate's transverse deflections due to uniformly distributed pressure are within set limits.To design the orifice plate, a symbolic solver (Wolfram Mathematica) is used to solve the governing fourth order differential equation of this problem (plate equation in polar coordinates), with appropriate boundary conditions. Results from the symbolic solver are juxtaposed with results from a GUI/Menu driven FEM package (Altair Hyperworks suite). Both the symbolic and menu driven solutions are compared with each other and with published relationships.Governing equations for bending of plates, in polar coordinates (for the orifice plate) have the need to resolve mathematical singularities for "1/r", for "r=0" type terms. This when reconciled using symbolic solvers allows a better grasp of the esoteric inter-relationships between various terms in the governing equations, which are akin to design variables. This allows students to use this esoteric knowledge to better apply GUI/menu driven solvers for engineering design.The primary pedagogical goal of this work allows the exertion of importance of governing equation based modeling to improve a "behind the scenes" understanding of GUI/menu driven FEM efforts. Students are made aware of the use of engineering standards and validation of numerical solutions based on numerical accuracy and convergence of solution through comparison with analytical data.

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Symbolic computation in structural engineering

Cited by 36 publications

References 77 publications

Symbolic Scientific Software Skills for Engineering Students

Symbolic Scientific Software Skills for Engineering Students

Exact integration of the stiffness matrix of an 8‐node plane elastic finite element by symbolic computation

Using Finite Element Methods to Calculate the Deflection of an Orifice Plate Subject to Uniform Pressure Distribution

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