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@mrrclb48z

simple beam,uniformly distributed load はりの応力とSFD,BMD 発展例題4.24 p102「材料力学演習」をsympyでやってみたい。

Last updated at Posted at 2023-12-19

パイソニスタの方へ
・??? 何かいい方法がありませんか。変な質問で申し訳ありません。
・私のver0.2の「symbol」の使い方を教えて下さい。(2023/12/22追加)
　以下で問い合わせ中。

・私のver0.3の「doble integral」の使い方を教えて下さい。(2023/12/24追加)
　あと2息です。

オリジナル

発展例題4.24 p102＜「材料力学演習(20221021)一括(ver.3.3)」を勉強したい。
　　　　　　　　　　？？？タブレット等で、pdfを開く事ができないかも。？？？　

latexで(勉強中)

(2023/12/26追加)
基本事項３の４関係式　P94より

\begin{array}{ll}
\dfrac{dQ}{dx}=q\\
\dfrac{dM}{dx}=Q\\
\end{array}

(2023/12/22追加)
・左端を揃えたいです。
・左端のスペースを削除したいです。

F = \left\{
\begin{array}{ll}
R_A & (0 \leq x \leq a)\\
R_A-q(x-a) & (a \leq x \leq l)
\end{array}
\right.

　　　　　　　Fを積分
　　　　　　　Mを微分

M = \left\{
\begin{array}{ll}
R_Ax & (0 \leq x \leq a)\\
R_Ax-1/2q(x-a)^2 & (a \leq x \leq l)
\end{array}
\right.

sympyで

ver0.3 重複積分法で

・「double integral」の使い方を教えて下さい。(2023/12/24追加)

# ver0.3 (2023/12/22追加)
# 発展例題4.24 p102

from sympy import *
from decimal import Decimal, ROUND_HALF_UP, ROUND_HALF_EVEN

var('l,q,a',real=True)
var('x'    ,real=True)
var('u,v'  ,real=True)
# var('RA'     ,real=True)
RA = Symbol('RA')
def myDic (myStrKey,myValue):
    return {sympify(myStrKey):myValue}
#
u0x = (u,0,x)
MAC = integrate(RA ,u0x)                    .simplify()               ;print("# MAC =",MAC)                      
FAC = diff(MAC,x)                           .simplify()               ;print("# FAC =",FAC)                      
# 
uav = (u,a,v)
vax = (v,a,x)
MCB = (MAC-integrate(integrate(q,uav),vax)) .simplify()               ;print("# MCB =",MCB)                      
FCB = diff(MCB,x)                           .simplify()               ;print("# FCB =",FCB)                      
RA  = solve(MCB.subs({x:l}),RA) [0]                                   ;print("# RA  =",RA );print()                     
# 
rep = {l:1.0,a:0.4,q:1670}
rep|= myDic("RA" ,RA.subs(rep).simplify() )                           ;print("# rep =",rep)
# 
print("# RA  =",Decimal(str(RA .subs(rep))).quantize(Decimal('0'), ROUND_HALF_UP))
print("# FAC =",Decimal(str(FAC.subs(rep))).quantize(Decimal('0'), ROUND_HALF_UP))
print("# FCB =",            FCB.subs(rep)  .simplify()                           )
print("# MAC =",            MAC.subs(rep)  .simplify()                           )
print("# MCB =",            MCB.subs(rep)  .simplify()                           )
# MAC = RA*x
# FAC = RA
# MCB = RA*x - a**2*q/2 + a*q*x - q*x**2/2
# FCB = RA + a*q - q*x
# RA  = q*(a**2 + l*(-2*a + l))/(2*l)

# rep = {l: 1.0, a: 0.4, q: 1670, RA: 300.600000000000}
# RA  = 301
# FAC = 301
# FCB = 968.6 - 1670*x
# MAC = 300.6*x
# MCB = -835*x**2 + 968.6*x - 133.6

ver0.2 うごきません。

・repに全部の値を、辞書へ。辞書から要素を取り出したい。
・変数RAを,varだと、RAでした。symbolで対応しました。

# ver0.2 (2023/12/22追加)
# 発展例題4.24 p102

from sympy import *

var('l,q,a'   ,real=True)
var('MAC,x'   ,real=True)
var('MCB'     ,real=True)
var('FAC,FCB' ,real=True)
var('RB'      ,real=True)
var('F0x'     ,real=True)
# var('RA'      ,real=True)
RA = Symbol('RA')

def myDic (myStrKey,myValue):
    return {sympify(myStrKey):myValue}
MAC = RA*x                                                           ;print("# MAC=",MAC)                                                              
MCB = solve(-RA*x-Rational(1,2)*q*(x - a)**2+MCB,MCB)[0]             ;print("# MCB=",MCB)
FAC = diff(MAC,x)                                                    ;print("# FAC=",FAC)
FCB = diff(MCB,x).simplify()                                         ;print("# FCB=",FCB)   
RA  = solve(MCB.subs({x:l}),RA)[0]                                   ;print("# RA =",RA )
RB  = q*(l - a)-RA                                                   ;print("# RB =",RB )
print()
rep={l:1.0,a:0.4,q:1.67*1000}                                     #  ;print("# ",rep )
rep |= myDic("RA" ,RA .subs(rep))                                 #  ;print("# ",rep )
rep |= myDic("FAC",FAC.subs(rep))                                 #  ;print("# ",rep )
rep |= myDic("RB" ,RB .subs(rep))                                 #  ;print("# ",rep )
rep |= myDic("FCB",FCB.subs(rep))                                 #  ;print("# ",rep )
rep |= myDic("MAC",MAC.subs(rep))                                 #  ;print("# ",rep )
rep |= myDic("MCB",MCB.subs(rep))                                    ;print("# ",rep,type(rep) )
print("# RA =",rep[RA]  )
# print("# RB =",rep[RB] )
# print("# FAC=",rep[FAC])
# print("# FCB=",rep[FCB])
# print("# MAC=",rep[MAC])
# print("# MCB=",rep[MCB])

# MAC= RA*x
# MCB= RA*x + q*(a - x)**2/2
# FAC= RA
# FCB= RA - q*(a - x)
# RA = -q*(a - l)**2/(2*l)
# RB = q*(-a + l) + q*(a - l)**2/(2*l)

#  {l: 1.0, a: 0.4, q: 1670.0, RA: -300.600000000000, FAC: -300.600000000000, RB: 1302.60000000000, FCB: 1670.0*x - 968.6, MAC: -300.6*x, MCB: -300.6*x + 835.0*(0.4 - x)**2} <class 'dict'>

File "/home/xxx/xxx.py", line 32, in
print("# RA =",rep[RA] )
KeyError: -q*(a - l)**2/(2*l)

ver0.1

# ver0.1 (2023/12/19作成)
# 発展例題4.24 p102
from sympy import *

var('l,q,a'   ,real=True)
var('MAC,RA,x',real=True)
var('MCB'     ,real=True)
var('FAC,FCB' ,real=True)
var('RB'      ,real=True)
var('F0x'     ,real=True)
def myEq_RepLR(eq):
     return {eq.lhs:eq.rhs}
eqMAC=Eq(MAC,RA*x)                                                ;print("#",eqMAC)
eqMCB=Eq(-RA*x+Rational(1,2)*q*(x-a)**2+MCB,0)                    ;print("#",eqMCB)
eqMCB=Eq(MCB,solve([eqMAC,eqMCB],MCB)[MCB])                       ;print("#",eqMCB)
eqFAC=Eq(FAC,diff(eqMAC.rhs,x))                                   ;print("#",eqFAC)
eqFCB=Eq(FCB,diff(eqMCB.rhs,x))                                   ;print("#",eqFCB)
eqRA =Eq(RA,solve(Eq(eqMCB.rhs.subs({x:l}),0),RA)[0].factor() )   ;print("#",eqRA ) 
print()
rep={l:1.0,a:0.4,q:1.67*1000}                                     ;print("#",rep )
eqRA =Eq(RA,eqRA.rhs.subs(rep))                                   ;print("#",eqRA)
eqRB =Eq(RB,solve(Eq(RB,q*(l-a)-RA),RB)[0])                       ;print("#",eqRB) 
eqRB =eqRB.subs(rep).subs(myEq_RepLR(eqRA))                       ;print("#",eqRB) 
eqFAC=eqFAC.subs(myEq_RepLR(eqRA))                                ;print("#",eqFAC)
eqFCB=eqFCB.subs(rep).subs(myEq_RepLR(eqRA))                      ;print("#",eqFCB)
eqMAC=eqMAC.subs(myEq_RepLR(eqRA))                                ;print("#",eqMAC)
eqMCB=eqMCB.subs(rep).subs(myEq_RepLR(eqRA))                      ;print("#",eqMCB)
print()
eqF0x=Eq(F0x,solve(Eq(eqFCB.rhs,0),x)[0])                         ;print("#",eqF0x)
# Eq(MAC, RA*x)
# Eq(MCB - RA*x + q*(-a + x)**2/2, 0)
# Eq(MCB, RA*x - a**2*q/2 + a*q*x - q*x**2/2)
# Eq(FAC, RA)
# Eq(FCB, RA + a*q - q*x)
# Eq(RA, q*(a - l)**2/(2*l))

# {l: 1.0, a: 0.4, q: 1670.0}
# Eq(RA, 300.6)
# Eq(RB, -RA - a*q + l*q)
# Eq(RB, 701.4)
# Eq(FAC, 300.6)
# Eq(FCB, 968.6 - 1670.0*x)
# Eq(MAC, 300.6*x)
# Eq(MCB, -835.0*x**2 + 968.6*x - 133.6)

# Eq(F0x, 0.58)

いつもの? sympyの実行環境と 参考のおすすめです。

(テンプレート)

いつもと違うおすすめです。

＞一部に等分布荷重を受ける単純支持はり
＞JSME p89
　
＞単純支持ばり 10)
＞構造力学公式集 p138

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