國立虎尾科技大學 |

Finite Element Concepts = A Closed-Form Algebraic Development /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Finite Element Concepts/ by Gautam Dasgupta.
其他題名:	A Closed-Form Algebraic Development /
作者:	Dasgupta, Gautam.
面頁冊數:	XXXVI, 333 p. 45 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Mechanical engineering. -
電子資源:	https://doi.org/10.1007/978-1-4939-7423-8
ISBN:	9781493974238

Finite Element Concepts = A Closed-Form Algebraic Development /
Dasgupta, Gautam.

Finite Element ConceptsA Closed-Form Algebraic Development /[electronic resource] :by Gautam Dasgupta. - 1st ed. 2018. - XXXVI, 333 p. 45 illus.online resource.

1. Bar -- 2. Trusses -- 3. 2-D Llinear Interpolation -- 4. Triangular Elements -- 5. Taig’s Convex Quadrilateral Elements -- 6. Irons patch test -- 7. Eight DOFs -- 8. Incompressibility -- 9. Conclusions.

This text presents a highly original treatment of the fundamentals of FEM, developed using computer algebra, based on undergraduate-level engineering mathematics and the mechanics of solids. The book is divided into two distinct parts of nine chapters and seven appendices. The first chapter reviews the energy concepts in structural mechanics with bar problems, which is continued in the next chapter for truss analysis using Mathematica programs. The Courant and Clough triangular elements for scalar potentials and linear elasticity are covered in chapters three and four, followed by four-node elements. Chapters five and six describe Taig’s isoparametric interpolants and Iron’s patch test. Rayleigh vector modes, which satisfy point-wise equilibrium, are elaborated on in chapter seven along with successful patch tests in the physical (x,y) Cartesian frame. Chapter eight explains point-wise incompressibility and employs (Moore-Penrose) inversion of rectangular matrices. The final chapter analyzes patch-tests in all directions and introduces five-node elements for linear stresses. Curved boundaries and higher order stresses are addressed in closed algebraic form. Appendices give a short introduction to Mathematica, followed by truss analysis using symbolic codes that could be used in all FEM problems to assemble element matrices and solve for all unknowns. All Mathematica codes for theoretical formulations and graphics are included with extensive numerical examples.

ISBN: 9781493974238

Standard No.: 10.1007/978-1-4939-7423-8doiSubjects--Topical Terms:

557493
Mechanical engineering.

LC Class. No.: TA329-348

Dewey Class. No.: 519

Finite Element Concepts = A Closed-Form Algebraic Development /
LDR:03045nam a22004095i 4500 001 997959
003 DE-He213
005 20200701010629.0
007 cr nn 008mamaa
008 201225s2018 xxu| s |||| 0|eng d
020 $a 9781493974238 $9 978-1-4939-7423-8
024 7 $a 10.1007/978-1-4939-7423-8 $2 doi
035 $a 978-1-4939-7423-8
050 4 $a TA329-348
050 4 $a TA640-643
072 7 $a TBJ $2 bicssc
072 7 $a TEC009000 $2 bisacsh
072 7 $a TBJ $2 thema
082 0 4 $a 519 $2 23
100 1 $a Dasgupta, Gautam. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1289351
245 1 0 $a Finite Element Concepts $h [electronic resource] : $b A Closed-Form Algebraic Development / $c by Gautam Dasgupta.
250 $a 1st ed. 2018.
264 1 $a New York, NY : $b Springer New York : $b Imprint: Springer, $c 2018.
300 $a XXXVI, 333 p. 45 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
505 0 $a 1. Bar -- 2. Trusses -- 3. 2-D Llinear Interpolation -- 4. Triangular Elements -- 5. Taig’s Convex Quadrilateral Elements -- 6. Irons patch test -- 7. Eight DOFs -- 8. Incompressibility -- 9. Conclusions.
520 $a This text presents a highly original treatment of the fundamentals of FEM, developed using computer algebra, based on undergraduate-level engineering mathematics and the mechanics of solids. The book is divided into two distinct parts of nine chapters and seven appendices. The first chapter reviews the energy concepts in structural mechanics with bar problems, which is continued in the next chapter for truss analysis using Mathematica programs. The Courant and Clough triangular elements for scalar potentials and linear elasticity are covered in chapters three and four, followed by four-node elements. Chapters five and six describe Taig’s isoparametric interpolants and Iron’s patch test. Rayleigh vector modes, which satisfy point-wise equilibrium, are elaborated on in chapter seven along with successful patch tests in the physical (x,y) Cartesian frame. Chapter eight explains point-wise incompressibility and employs (Moore-Penrose) inversion of rectangular matrices. The final chapter analyzes patch-tests in all directions and introduces five-node elements for linear stresses. Curved boundaries and higher order stresses are addressed in closed algebraic form. Appendices give a short introduction to Mathematica, followed by truss analysis using symbolic codes that could be used in all FEM problems to assemble element matrices and solve for all unknowns. All Mathematica codes for theoretical formulations and graphics are included with extensive numerical examples.
650 0 $a Mechanical engineering. $3 557493
650 0 $a Applied mathematics. $3 1069907
650 0 $a Engineering mathematics. $3 562757
650 0 $a Partial differential equations. $3 1102982
650 0 $a Computer mathematics. $3 1199796
650 0 $a Civil engineering. $3 561339
650 1 4 $a Mathematical and Computational Engineering. $3 1139415
650 2 4 $a Partial Differential Equations. $3 671119
650 2 4 $a Computational Science and Engineering. $3 670319
650 2 4 $a Mechanical Engineering. $3 670827
650 2 4 $a Civil Engineering. $3 669250
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9781493974214
776 0 8 $i Printed edition: $z 9781493974221
776 0 8 $i Printed edition: $z 9781493984817
856 4 0 $u https://doi.org/10.1007/978-1-4939-7423-8
912 $a ZDB-2-ENG
912 $a ZDB-2-SXE
950 $a Engineering (SpringerNature-11647)
950 $a Engineering (R0) (SpringerNature-43712)