Code_Aster. Graphic charter for the realization of the formulas mathematics in documentation Code_Aster

Transcription

1 Ttre : Charte graphque pour la réalsaton des formules [...] Date : /1/008 Page : 1/15 Organzaton (S):EDF/IMA/MMN Data-processng Manuel de Descrptf D8.01 booklet: Presentaton of documentaton D document Graphc charter for the realzaton of the formulas mathematcs n documentaton Summary After havng dentfed the mathematcal objects mnmal generals most commonly employed by the communty of the mechancs developng n Aster, j M M j C K x k ( ) e.g( P) one exposes the nstructons of strkng of the mathematcal formulas whch allow on the one hand one returned paper and acceptable screen ( T ) dv ( T ) grad T f( t ) and whch, n addton, answers the crtera requred n the nternatonal publcatons dealng wth the mechancs of the sold. k 1 n j Warnng : The translaton process used on ths webste s a "Machne Translaton". It may be mprecse and naccurate n whole or n part and s provded as a convenence. Copyrght 019 EDF R&D - Lcensed under the terms of the GNU FDL (

2 Ttre : Charte graphque pour la réalsaton des formules [...] Date : /1/008 Page : /15 In documentaton Aster, the mathematcal formulas are developed under the Equaton edtor of Mcrosoft Word5 (verson of MathType Edtor Equaton of Desgn Scence Inc). Warnng : The translaton process used on ths webste s a "Machne Translaton". It may be mprecse and naccurate n whole or n part and s provded as a convenence. Copyrght 019 EDF R&D - Lcensed under the terms of the GNU FDL (

3 Ttre : Charte graphque pour la réalsaton des formules [...] Date : /1/008 Page : /15 1 Sprt and carred 1.1 Constrants mposed by the projecton of the dgtal documents Aster on a meda Part of the nstructons for the draftng of the formulas n the documents wth the formalsm Aster, was controlled by the concern to keep an acceptable esthetcs and a legblty ndependently of the meda and the basc polce of the surroundng text. In the current state of the art as regards physcal representaton of the formulas n the electronc documents, n the absence of DTD (Descrpton of the Type of Document to formalsm SGML), those are comparable to drawngs. They thus do not undergo reformatng accordng to the meda of consultaton (paper, cathode screens). The e-book comprses as many external fles of formulas (drawngs). The contents of these fles come to be dsplayed wth the consultaton of the book to the ste whch t must have n the text. The book comprses a table connectng the name of the fle (the formula) and the poston n the book. 1. Standards and recommendatons Aster They ndcate the manner typographcally of representng the types of the mathematcal objects most frequently handled by the mechancs of the sold. The prncple s the use of typographcal enrchments Italc and Fat to typfy these objects. The wrter Aster wll use of these recommendatons whch consttute an acceptable mnmal representaton by the communty of the mechancs of the sold developng n Aster. They: approach returned the Tex traner, take as a startng pont the necessary rules to publsh n the followng revews: - Comp. Meth. Appl. Mech. Eng. - Int. J. Num. Meth. Eng. - ASME J. Appl. Mech. - Europ. J. Mech. A/Solds. take account of the possbltes and lmtatons of the Equaton edtor of Mcrosoft Word5. What gves for example: j M M j C K x k ( ) e.g( P) (calculaton carred out by the operator DYNA_LINE_HARM [U ]) k 1 ( T ) dv ( T ) grad T f( t ) (calculaton carred out by the operator THER_NON_LINE [U4..0 1]) ou 1 VM j tr( j j 1, n j Warnng : The translaton process used on ths webste s a "Machne Translaton". It may be mprecse and naccurate n whole or n part and s provded as a convenence. Copyrght 019 EDF R&D - Lcensed under the terms of the GNU FDL (

4 Ttre : Charte graphque pour la réalsaton des formules [...] Date : /1/008 Page : 4/15 (calculaton carred out by the operand INVARIANT procedure POST_RELEVE [U4.74.0]). Warnng : The translaton process used on ths webste s a "Machne Translaton". It may be mprecse and naccurate n whole or n part and s provded as a convenence. Copyrght 019 EDF R&D - Lcensed under the terms of the GNU FDL (

5 Ttre : Charte graphque pour la réalsaton des formules [...] Date : /1/008 Page : 5/15 Typographcal realzaton of the formulas n Aster After havng dentfed the mathematcal objects selected, one enumerates enrchments whch apply to t, the polce to be used, the bodes, the relatve postons of the elements whch compose the formulas (ndces, exponents, symbols of relatons, etc )..1 Enrchments and mathematcal types of objects The table hereafter summarzes on the objects selected, the basc typographcal achevements that the wrter Aster wll employ as far as possble. Type of object Ital Rom anan Fat Mag Polce Number X X Tmes Scalar varable X X Tmes or Symbol (1) Usual functon X X Tmes () Functon wth X X Tmes or Symbol scalar value Functon wth vectoral or X X Tmes or Symbol () tensoral values Tensor, Matrx, vector (dmenson and more) X X Tmes or Symbol () Space of scalars or X X DESCARTES (4) vectors Space of functons X X Corsva monotype (5) Text X X Geneva (6) 1) If a Greek captal letter s employed for a scalar varable then to always strke t as a Roman. ) The Equaton edtor of Word5 can recognze the name of about forty usual functons lke: det, lm, cos, Im etc ) For the Symbol polce, t Fat appears on the screen but not clearly wth the mpresson. Example: (fat), (not fat). 4) Body of realtes, complexes ç, entretes ı. One can have dffculty of prntng the polce DESCARTES when t s employed n the Equaton edtor. The prnter replaces the characters DESCARTES by a whte. Unknown remedy for the date of publcaton of ths document. To address tself to the Person n charge of Documentaton Aster. 5) For example: (F), (here Body 18) to note a space of functons, (P) a problem, (S) a system. 6) Accordng to MacOS and the versons of Word5 and the Equaton edtor whch one lays out t s possble that Geneva n a text of formula left on the prnter n Courer. To prefer then Helvetca who does not present ths dsadvantage. Cauton Warnng : The translaton process used on ths webste s a "Machne Translaton". It may be mprecse and naccurate n whole or n part and s provded as a convenence. Copyrght 019 EDF R&D - Lcensed under the terms of the GNU FDL (

6 Ttre : Charte graphque pour la réalsaton des formules [...] Date : /1/008 Page : 6/15 It results from 4 and 5 that the operatng systems MacOS of the wrters Aster wll have to be rgged by ths polce. Warnng : The translaton process used on ths webste s a "Machne Translaton". It may be mprecse and naccurate n whole or n part and s provded as a convenence. Copyrght 019 EDF R&D - Lcensed under the terms of the GNU FDL (

7 Ttre : Charte graphque pour la réalsaton des formules [...] Date : /1/008 Page : 7/15. Examples for the functons Dm. of spaces Wrtng of the applcaton Physcal examples f(x) b f E(T)YOUNG modulus functon of the temperature n f(t) b f g(s) y n m f(t) V f K(s) Geometrcal rgdty m f(a) T f A(T) Elastcty functon of the temperature. Body of the components of the formulas Elements of the formula Body Examples Normal terms (*) Exponents and ndces Symbols 1 Pt 9 Pt 18 Pt Under symbols 1 Pt (*) If one uses Corsva monotype for a normal term, to prefer the body 14 Pt. That s to say the adjustment followng n the headng menu of the Edtor of Mathematcal formulas Warnng : The translaton process used on ths webste s a "Machne Translaton". It may be mprecse and naccurate n whole or n part and s provded as a convenence. Copyrght 019 EDF R&D - Lcensed under the terms of the GNU FDL (

8 Ttre : Charte graphque pour la réalsaton des formules [...] Date : /1/008 Page : 8/15.4 Relatve postons of the elements of a formula It s necessary to understand by there, the relatve poston of the ndces and exhbtors compared to the term whch they affect and the relatve poston of the lnes of equatons or the lnes and columns of matrces. One takes the values by of the equaton edtor of Mcrosoft Word5 expressed hereafter n % of the body of the symbols. That s to say the adjustment followng n the headng menu of the Edtor of mathematcal formulas.5 Style sheet for the formulas Headng menu of the Edtor of mathematcal formulas.6 Spaces on both sdes of sgn = One recommends to solate the sgn well = whle havng whte on both sdes of sgn suffcently. Goal : to make qute readable the two members of the equatons. One recommends to add to affected spacng by automatcally by the Equaton edtor after the sgn of relaton = a whte of a quadratn. Warnng : The translaton process used on ths webste s a "Machne Translaton". It may be mprecse and naccurate n whole or n part and s provded as a convenence. Copyrght 019 EDF R&D - Lcensed under the terms of the GNU FDL (

9 Ttre : Charte graphque pour la réalsaton des formules [...] Date : /1/008 Page : 9/15.7 Texts n the formulas If the author wshes to accompany hs formula by a text (what s dsadvsed) for, for example, to clarfy certan terms, ths text wll be n Geneva 10 Roman nonfatty Style Text of the style sheet of the Equaton edtor (wth the reserves expressed n [.1]). In ths case, the unt formulates + text forms only one graphc block. j M M j C K x k ( ) e.g( P).8 Formulas except text and n text où C k 1 Matrce d' Amortssement The typography of the terms of formulas ntegrated n a paragraph s the same one as n the formula t even. An example s gven n [.6]. n j Recommendatons and advce.1 Notatons author --> reader At the top of document the wrter wll expose hs notatons, manly n what they dffer or supplement the recommendatons Aster. He wll take care to choose a symbolsm present n the Equaton edtor of Word.. Notatons author --> typst The wrter wll ndcate on hs manuscrpt, by a code wth hm the nstructons of enrchment of the terms of ts mathematcal formulas.. The Transposed sgn Transposed of a matrx or a vector (and opposte of matrx) as follows: T 1 T T M, M, M, x. Modal mass for the mode : u Mu.4 Tny Greek In the Symbol polce one wll prefer the tny ph wth to avod confusons T Warnng : The translaton process used on ths webste s a "Machne Translaton". It may be mprecse and naccurate n whole or n part and s provded as a convenence. Copyrght 019 EDF R&D - Lcensed under the terms of the GNU FDL (

10 Ttre : Charte graphque pour la réalsaton des formules [...] Date : /1/008 Page : 10/15.5 Functons and varables Not to confuse the functon and ts realzaton for a gven value of ts varable. To always ndcate what depend the functons the frst tme that the functon appears. Example:.6 Derved 1 g(, ) ( (tr ) Id) y ( ) (Crteron of plastcty) To ndcate where are taken the dervatve, at least durng ther frst appearance. The followng formalsm s recommended: that s to say the functon g(,), ts partal dervatve compared to for and s wrtten: g or ths one for an equlbrum equaton. (, ) j, j f 0 Warnng : The translaton process used on ths webste s a "Machne Translaton". It may be mprecse and naccurate n whole or n part and s provded as a convenence. Copyrght 019 EDF R&D - Lcensed under the terms of the GNU FDL (

11 Ttre : Charte graphque pour la réalsaton des formules [...] Date : /1/008 Page : 11/15.7 Conventon of the repeated ndces In a ndcelle notaton, one wll use the conventon of EINSTEIN known as repeated ndces. Ths conventon, makes t possble to reduce the wrtng and to be freed from employment from the symbol from summaton. Prncple : an ndex repeated twce, once n top, once n bottom, or more smply twce n bottom, ndcates automatcally a summaton (1,, N). Example: v v e v e n 1 v, vector v, components e, basc vector tr k k 1 1 tr trace du tenseur Id. j j k k... j1 j j j j or more smply.. j j.8 Greek ndces and Latn ndces One advses the use the ndex Greek (,, etc ) for a course n the nterval {1, } and Latn ndces (, j, k, etc ) n the nterval {1,.}..9 Algnment and balance of the equatons To adopt a provson such as the smlar terms are on the same balance. U z 0 j U j Z 0 j j Z 0 réf U dl kl T T k jl o A E K U A E K U U z j U j Z j Z 0 j Z réf U dl kl T T k jl o A E K U A E K U 0 0 Warnng : The translaton process used on ths webste s a "Machne Translaton". It may be mprecse and naccurate n whole or n part and s provded as a convenence. Copyrght 019 EDF R&D - Lcensed under the terms of the GNU FDL (

12 Ttre : Charte graphque pour la réalsaton des formules [...] Date : /1/008 Page : 1/15 4 Examples These examples are extracted from the sotropc form of thermoelastcty. j D j 1 kkj VM. éq D D. tr 1 I, J I J D D. éq VM 4.1 Thermodynamc potental, densty of free energy D 1 réf 1 C, T tr j j K T T tr T réf. F T T K C, T tr j D j D K T T réf 1. tr T réf F T T Stablty: postve defnte potental: 0 ; K 0 E 0 ; 1 0, 5 4. Complementary potental, densty of enthalpy free D F * F * réf C, T tr j j T T tr T réf 1 1. E E T T, 1 tr 1 T T T tr C j D j D réf 1. T réf 18K 4 T T Warnng : The translaton process used on ths webste s a "Machne Translaton". It may be mprecse and naccurate n whole or n part and s provded as a convenence. Copyrght 019 EDF R&D - Lcensed under the terms of the GNU FDL (

13 Ttre : Charte graphque pour la réalsaton des formules [...] Date : /1/008 Page : 1/15 4. Coeffcents of elastc rgdty D F j, T j jkl réf j j kl k jl réf T T D kl K T T kl j 4.4 Relatons stress-strans D K T T j kk j j réf j E E tr T T j j j réf j K T T réf Warnng : The translaton process used on ths webste s a "Machne Translaton". It may be mprecse and naccurate n whole or n part and s provded as a convenence. Copyrght 019 EDF R&D - Lcensed under the terms of the GNU FDL (

14 Ttre : Charte graphque pour la réalsaton des formules [...] Date : /1/008 Page : 14/ Relatons deformaton-constrants D réf 1 T T j E E j kk j j E T T réf Elastc plane constrants D E E T T réf COPL T T D réf COPL réf E 1 E T T Complementary potental D F * DEPL 1 1 tr D E E Warnng : The translaton process used on ths webste s a "Machne Translaton". It may be mprecse and naccurate n whole or n part and s provded as a convenence. Copyrght 019 EDF R&D - Lcensed under the terms of the GNU FDL (

15 Ttre : Charte graphque pour la réalsaton des formules [...] Date : /1/008 Page : 15/15 Intentonally whte page. Warnng : The translaton process used on ths webste s a "Machne Translaton". It may be mprecse and naccurate n whole or n part and s provded as a convenence. Copyrght 019 EDF R&D - Lcensed under the terms of the GNU FDL (