JP4009123B2 - Method and program for determining the shape of a railway vehicle structure - Google Patents

Description

【００２２】
本実施の形態では、平均コンプライアンスが与えられた制約条件（体積、部分的な構体厚の固定、構体厚の最小値など）のもとで最小化された状態を最適であるとしている。平均コンプライアンスの最小化に関しては、例えば、日本機械学会論文集（Ａ編）６０巻５７８号（１９９４−１０）第１４４〜１５０頁に掲載する「線形弾性問題における領域最適化解析」に掲載されており、本実施の形態では、「線形弾性問題における領域最適化解析」に基づいて解析を行うプログラムを使用して鉄道車両用構体形状の最適化を図っている。尚、このプログラムは、コンピュータ３０の記憶装置３３に記憶されている。
【００２３】
「線形弾性問題における領域最適化解析」では、線形弾性体の領域形状を設計変数にした領域最適化問題を連続体のままで定式化しておいて、分布系の最適化理論を適用することによって導出される領域変動の支配方程式を基礎にして領域最適化問題にアプローチしている。数値解析法は、支配方程式を解くための方法として定式化され、その１つの方法として力法が提案されている。力法は、領域変動の支配方程式を線形弾性問題の境界値問題に置き換えて解くために、有限要素法などが利用できる点で実用的である。支配方程式に現れる形状勾配関数も有限要素法などを利用して解析することができる。
そこで、「線形弾性問題における領域最適化解析」は、平均コンプライアンスの最小化問題を定式化し、それに対する最適性基準と最適化基準に基づいて算出される形状勾配関数を明らかにした上で、形状勾配関数を用いた力法を線形弾性体の領域問題に適用している。
【００２４】
線形弾性連続体の領域最小化問題を取り扱うのに際して、「線形弾性問題における領域最適化解析」では、平均コンプライアンスを目的汎関数に選んでいる。この場合、後で示すように領域最適化問題が自己随伴問題となり、形状勾配関数が線形弾性変形の解である変位だけによって評価できることになる。この意味で、平均コンプライアンスは力学的に単純な目的汎関数であると考えることができる。
【００２５】
平均コンプライアンスの最小化問題は、次のようにして定式化される。
線形連続体に作用する外力と物体力との関係は数４のようになり、線形連続体を変位させる重力などの関係は、数５のようになる。ここで、Ωは領域を示し、ｕは線形連続体の変位を示し、ｆは物体力を示し、ｈは強制変位を示し、Ｐは表面力を示している。境界値問題に対する弱形式あるいは変分形式は、数２のように表される。
【００２６】
【数２】

【００２７】
但し、双一次形式ａ（υ，ω）と一次形式ｌ（ω），ｌ_h（ω）は数３〜数５のように定義する。
【００２８】
【数３】

【数４】

【数５】

【００２９】
また、Ｈｏｏｋｅ剛性Ｃ∈Ｌ∽（Ω；Ｒⁿ⁴）は次のような対称性と正定値性を次式のように仮定している。ここで、Ｌ∽（Ω；Ｒⁿ）は、有界可積分Ｌｅｂｅｓｇｕｅ関数空間を表す。
【００３０】
【数６】

【００３１】
そして、分布関数Ｃ，ｆ，ｈ，Ｐが領域変動に対して一意に決定されると仮定すると、仮定した領域変動に対して、一意に決定されるＣ∈Ｃ¹（Ｄ；Ｒⁿ⁴），ｆ，ｈ，Ｐ∈Ｃ¹（Ｄ；Ｒⁿ）と領域の大きさに対する上限値Ｍ∈Ｒ₊が与えられているとき、平均コンプライアンスは数７のように表される。
【００３２】
【数７】

【００３３】
そして、数７で表される平均コンプライアンスが最小となる領域Ω₃を求める場合には、数８に示す状態方程式及び数９に示す質量制約を満たす必要がある。
【００３４】
【数８】

【数９】

【００３５】
次に、最適性基準を求める。
最適性基準は、Ｌａｇｒａｎｇｅ定数を適用して導出される。数８の等式制約条件式のＬａｇｒａｎｇｅ定数にはωを利用して、数９の不等式制約条件式のＬａｇｒａｎｇｅ定数にはΛを用いると、平均コンプライアンスの最小化問題は、数１０に示すＬａｇｒａｎｇｅ関数の停留化問題に書き換えることができる。
【００３６】
【数１０】

【００３７】
Ｌａｇｒａｎｇｅ関数の領域変動に対する導関数は数１１のように表すことができる。
【００３８】
【数１１】

【００３９】
ここで、Ｃ，ｆ，ｈ，Ｐが領域変動に対して一意であれば、ｌ_G（Ｖ）はベクトル関数Ｇを係数関数とする速度場Ｖの一次形式で数１２のように与えられることになる。
【００４０】
【数１２】

【００４１】
Ｇは、領域変動を与える速度場に対する目的汎関数の感度係数を与えるベクトル関数という意味で、形状勾配関数と呼ばれ、Ｃ，ｆ，ｈが空間固定、ｈ＝ｏｉｎＤ、物質共変Ｐ＋Ｐ_kυ_n＝ｏ（つまり、場所によって重力や物性が変化しないこと）と仮定したときのＧを具体的に求めると、数１３のようになる。
【００４２】
【数１３】

【００４３】
ここで、Ｌａｇｒａｎｇｅ関数Ｌの停留条件は、数１１に基づいて数１４〜数１８のようになる。
【００４４】
【数１４】

【数１５】

【数１６】

【数１７】

【数１８】

【００４５】
数１４から数１８を見ると、数１４は数２に示す状態方程式υ＝ｕ−ｈと一致したｖの支配方程式になっている。また、数１５は、ωについての支配方程式になっている。両者を比較すると 数１９に示す関係が得られる。
【００４６】
【数１９】

【００４７】
そして、計算を簡略化するために物体力は考えず、また、数１９を数１３に適用すると、数２０の関係が得られる。
【００４８】
【数２０】

【００４９】
かくしてＬａｇｒａｎｇｅ関数の導関数が形状勾配関数Ｇを係数とする速度場Ｖの一次形式で与えられたので、形状勾配関数Ｇを用いた力法の適用が可能となる。力法では、初期領域Ωからｋ回目の領域変動を行うことを考えたときの領域変動を表すＶ^(k)を数２１に示す支配方程式に基づいて解析する。
【００５０】
【数２１】

【００５１】
数２１に示す支配方程式で決定された領域変動Ｖ^(k)は、Ｌａｇｒａｎｇｅ関数Ｌを減少させる。すなわち、数２１に示す領域変動解析の支配方程式は、境界あるいは領域に力−Ｇを作用させたときの変位分布として領域変動を与える速度場Ｖが解析されることを示している。
【００５２】
続いて、本実施の形態の鉄道車両用構体形状の決定方法について、図面を参照しながら説明する。図１は、鉄道車両用構体形状の決定方法のフローチャートであり、図５は、図４のＨ部を示すものであって、有限の要素を仮想的に表した概念図である。
鉄道車両用構体形状の決定方法は、コンピュータ３０のＣＰＵ３１が記憶手段３３からプログラムを読み込んで、図１に示すフローチャートの処理を実行することにより行われる。そこで、鉄道車両用構体形状の決定方法では、まず、図１のステップ１（以下、「Ｓ１」いう。）において初期形状解析モデル（有限要素法）を入出力装置３２から入力し、記憶装置３３に記憶する。
【００５３】
具体的には、図５に示すように、鉄道車両用構体２０の全体を有限な要素Ｅに分割し、各要素Ｅの節点●に座標データを付け、例えば、４個の節点●（ｉ〜ｌ）を一組にする旨の有限要素法の要素情報を入力する。そして、外側面板６と内側面板７で構成される構体厚Ａ（図１１参照）の初期値を５０ｍｍに設定し、鉄道車両用構体２０の材料特性としてアルミニウム合金のヤング率及びポアソン比を入力する。そして、強度解析などを行う際に利用される境界条件として拘束条件と荷重条件を入力する。拘束条件としては、図４に示す台枠側梁に相当する部分２５を固定すること、及び、鉄道車両用構体２０の中心線Ｍに対称条件を加えることを入力する。ここで、対称条件を加えるのは、演算量を減らして、演算時間を短縮するためである。また、荷重条件としては、気密荷重を想定して鉄道車両用構体２０の外側に等分布荷重Ｓを与えることを入力する。
【００５４】
次に、Ｓ２において、鉄道車両用構体２０の強度解析を行う。強度解析は、コンピュータ３０のＣＰＵ３１がＳ１で記憶装置３３に記憶された初期形状解析モデルを読み出し、それに基づいて各要素Ｅ毎の歪量及び発生応力を算出して行う。
【００５５】
次に、Ｓ３において、感度解析を行う。感度解析では、コンピュータ３０のＣＰＵ３１が形状勾配関数Ｇを上記力法を利用した数２２に基づいて求める。
【００５６】
【数２２】

【００５７】
この数２２から求められる形状勾配関数Ｇは、図５に示す各要素Ｅの境界面上に分布する法線方向を向いたベクトル関数である。ここで、式に現れる変数の値は、Ｓ２の強度解析の解析結果から得られるものであり、ｆは物体力、ｅは弾性テンソル、ｕは変位、ΛはＬａｇｒａｎｇｅ定数である。
【００５８】
そして、Ｓ４において、収束判定を行う。収束判定は、感度解析を実行して得られた感度が十分小さいか否かで判断される。感度が十分小さいと判断した場合には（Ｓ４：ＹＥＳ）、処理を終了する。一方、感度が十分小さくないと判断した場合には（Ｓ４：ＮＯ）、Ｓ５へ進み、形状変更における制約条件が入力されているか否かを判断する。制約条件が入力されていると判断した場合（Ｓ５：ＹＥＳ）には、そのままＳ７へ進む。
【００５９】
一方、制約条件が入力されていないと判断した場合（Ｓ５：ＮＯ）には、Ｓ６において、制約条件として形状の変更を許さない点、移動方向の制約、体積（三次元の問題）又は面積（二次元の問題）を入出力装置３２から入力して記憶装置３３に記憶させてから、Ｓ７へ進む。具体的な制約条件としては、例えば、側構体２１と屋根構体２３を構成する中空形材５の外側面板６（図１１参照）から４０ｍｍの厚さに位置する節点●の移動を許さないこと、各要素Ｅの節点を（図５参照）をｘ方向のみに（一次元的に）移動させること、及び、外側面板６と内側面板７で囲まれる面積を初期形状と同一にすることを入力する。ここで、側構体２１と屋根構体２３を構成する中空形材５の外側面板６（図１１参照）から４０ｍｍの厚さを固定するとしたのは、構体厚Ａが４０ｍｍ以下になることを回避するためである。また、各要素Ｅの節点を（図５参照）をｘ方向のみに（一次元的に）移動させるのは、各要素Ｅを構体厚Ａ方向に伸縮させるようにして車両外形線を変動させないようにするためである。
【００６０】
そして、Ｓ７において、鉄道車両用構体２０の形状を変更する。具体的には、コンピュータ３０のＣＰＵ３１は、記憶装置３３に記憶された制約条件を読み出し、形状勾配関数Ｇの大きさに比例して各要素Ｅの境界面に力を加えて、節点●（図５参照）を移動させ、記憶装置３３に記憶された節点●の座標データを書き換える。これにより、各要素Ｅの大きさや形状が変わり、鉄道車両用構体２０の形状が初期形状と変化する。鉄道車両用構体２０の形状を変更したら、Ｓ３へ戻って処理を繰り返す。
【００６１】
こうした鉄道車両用構体形状の決定方法は、以下のように動作する。
図４に示すように、一様な構体厚Ａで形成された初期形状の鉄道車両用構体２０を有限な要素Ｅに分割し、各節点●の座標データ、有限要素法の要素情報、アルミニウム合金のヤング率・ポアソン比などの初期形状解析モデルを入力して強度解析を求め、初期形状解析モデル及び強度解析結果に基づいて形状勾配関数Ｇを求める（Ｓ１〜Ｓ３）。
【００６２】
収束判定において感度が十分に小さくない場合、すなわち、形状勾配関数Ｇが急激な勾配を有する場合には、制約条件に基づいて鉄道車両用構体２０の形状を変更する（Ｓ４：ＮＯ、Ｓ５：ＹＥＳ、Ｓ７）。
具体的には、例えば、形状勾配関数Ｇが局部的に大きい場合は、その形状勾配関数Ｇが大きい部分について、側構体２１及び屋根構体２３の外側から４０ｍｍの節点●を移動させないことや、節点●の移動方向がｘ方向に限定されていることなどの制約条件に基づいて、側構体２１及び屋根構体２３の内側から１０ｍｍ以内の部分における要素Ｅの節点●を内向きに移動させ、要素Ｅの大きさを小さくして要素数を増やす。また、外側面板６と内側面板７との間の面積が一定である制約条件があるので、形状勾配関数Ｇが小さい部分について、側構体２１及び屋根構体２３の内側から１０ｍｍ以内の部分における要素Ｅの節点●を外向きに移動させ、要素Ｅの大きさを大きくして要素数を減らす。こうして要素Ｅの分割方法を変更したら、移動させた節点●の座標データを書き換える。これにより、要素数が増加した部分は構体厚Ａが厚くなり、要素数が減少した部分は構体厚Ａが薄くなるため、初期形状の鉄道車両用構体２０の形状が変更される。鉄道車両用構体２０の形状を変更したら、Ｓ３へ戻って処理を繰り返す。これら一連の処理は、収束判定において感度が十分小さいと判断されるまで自動的に行われる。
【００６３】
そして、収束判定において感度が十分小さくなったと判断された場合、すなわち、形状勾配関数Ｇの勾配が小さくなった場合には、処理が終了し（Ｓ４：ＹＥＳ）、図３に示すように最適化された鉄道車両用構体１０が入出力装置３２に出力される。つまり、図４に示す鉄道車両用構体２０では、例えば、側構体２１と屋根構体２３との連結部分、すなわち、構体の折れ曲がった部分（以下、「肩部」という。）２４に外圧が負荷された場合は、外側面板６に引張応力が作用し、内側面板７に圧縮応力が発生するため、疲労破壊しやすいが、図１に示す処理を実行することにより、図４に示す鉄道車両用構体２０の肩部２４が、図３に示す鉄道車両用構体１０の肩部１４のように肉厚にされる。その反面、図３に示す鉄道車両用構体１０では、肩部３４の両端に相当する部分１６，１７が図４に示す鉄道車両用構体２０より肉薄にされる。
【００６４】
ところで、発明者は、最適化された鉄道車両用構体１０の変位及び応力に関する特性を確認するために、図４に示す初期形状の鉄道車両用構体２０と図３に示す最適化された鉄道車両用構体１０の変位量を比較した。図６は、初期形状の鉄道車両用構体２０の変位図であり、点線で原型を示し、実線で変形状態を示す。図７は、最適化された鉄道車両用構体２０の変位図であり、点線で原型を示し、実線で変形状態を示す。
【００６５】
本実験では、鉄道車両用構体１０，２０の外側に９８ｋＰａの等分布荷重を与えた。
その結果、初期形状の鉄道車両用構体２０では、図６に示すように、側構体２１は殆ど変形せず、鉄道車両用構体２０の肩部２４から屋根構体２３が大きく変形している。特に、屋根構体２３の中心部で変形が大きく、その変位量Ｔ１は約３．２７ｍｍである。それに対して、最適化された鉄道車両用構体１０では、図７に示すように、側構体１及び屋根構体３の全体が変形しており、歪みを側構体１と屋根構体３に分散させている。そのため、屋根構体３の中心部では、変位量Ｔ２が約１．４８ｍｍである。
よって、最適化された鉄道車両用構体１０と初期形状の鉄道車両用構体２０の屋根構体３，２３の中心部における変位を比較すると、最適化された鉄道車両用構体１０は、初期形状の鉄道車両用構体２０より変位量が約５５％減少することが判明した。
【００６６】
また、発明者は、初期形状の鉄道車両用構体２０と最適化された鉄道車両用構体１０における応力分布についても調べた。図８は、初期形状の鉄道車両用構体２０の側構体２１及び屋根構体２３の最大応力を示す応力図であり、図９は、最適化された鉄道車両用構体１０の側構体１及び屋根構体３の最大応力を示す応力図である。
【００６７】
本実験では、鉄道車両用構体１０，２０の外側に９８ｋＰａの等分布荷重を与えた。
その結果、初期形状の鉄道車両用構体２０では、図８に示すように、肩部２４において、外側面板６で発生する応力より内側面板７で発生する応力の方が低くなっていることがわかる。このように外側面板６と内側面板７とで発生する応力が不均衡であると、応力の低い内側面板７に応力が集中し、内側面板７が疲労破壊しやすい問題がある。それに対して、最適化された鉄道車両用構体１０では、図９に示すように、肩部１４において、外側面板６と内側面板７で発生する応力が殆ど均一であり、外側面板６と内側面板７のいずれか一方に応力が集中する問題が回避されている。そして、最適化された鉄道車両用構体１０は、側構体１が初期形状の鉄道車両用構体２０の側構体２１より肉薄になっても、初期形状の鉄道車両用構体２０の側構体２１とほぼ同じ応力が発生している。
よって、最適化された鉄道車両用構体１０は、初期形状の鉄道車両用構体２０と比較して、荷重負担の大きい部分を肉厚にして強度・剛性を向上させる一方、荷重負担の小さい部分を強度・剛性を維持した状態で肉薄にするので、構体の強度・剛性を向上させつつ、構体重量の増加を抑えられることがわかる。
【００６８】
よって、本実施の形態の鉄道車両用構体１０は、初期形状の鉄道車両用構体２０に一定の応力が外部と内部から作用することを条件として、鉄道車両用構体２０を有限な要素Ｅに分割し、形状勾配関数Ｇを算出して、形状勾配関数Ｇの演算結果が収束するように、すなわち、各要素ごとに歪量と歪量から計算される応力の積を算出し、その総和が小さくなるように鉄道車両用構体２０の形状を変化させるので、構体に発生した歪みが構体全体に分散され、外側面板６や内側面板７の板厚Ｂ，Ｃ（図１１参照）を一様に厚くしなくても、構体の強度・剛性を確保することができる。
【００６９】
その際、外側面板６の形状を一定とし、内側面板７の形状を変えて、初期形状の鉄道車両用構体２０の形状を変えるので、最適化された鉄道車両用構体１０は、初期形状の鉄道車両用構体２０の外形線を変えることなく、構体厚Ａを変化させており、各々の鉄道車両用構体２０の外形線に合わせて、構体の強度・剛性を確保することができる。
【００７０】
また、外側面板６と内側面板７との間の面積が一定になるように初期形状の鉄道車両用構体２０の形状を変更しており、一の要素Ｅの形状を大きくすると、他の要素Ｅの形状が小さくなり、外側面板６と内側面板７とで形成される構体厚Ａが必要以上に厚くなることがないので、構体全体の強度・剛性を確保しても、構体重量が殆ど増加せず、軽量化を実現することができる。
【００７１】
そして、最適化された鉄道車両用構体１０では、構体各部の歪量に応じて構体各部の構体厚Ａを変えられているので、外側面板６や内側面板７の板厚を一様に厚くしなくても、構体の強度・剛性を確保することができる。
【００７２】
また、最適化された鉄道車両用構体１０では、例えば、肩部１４は、外側面板６が引張荷重を受け、内側面板７が圧縮荷重を受けるが、それらの荷重に対応しうるように肉厚に形成しており、必要な部分の構体厚Ａを必要な分だけ厚くしているので、構体の強度・剛性の確保と軽量化とを十分実現することができる。また、肩部２４に接続する部分１６，１７を強度・剛性を確保した状態で肉薄にするので、構体全体の強度・剛性を確保しても、構体重量が殆ど増加せず、軽量化を実現することができる。
【００７３】
なお、本発明は、実施形態のものに限定されるわけではなく、その趣旨を逸脱しない範囲で様々な変更が可能であることはいうまでもない。
【００７４】
【発明の効果】
従って、本発明は、外側面板と内側面板と中板とで形成される中空形材を用いた鉄道車両用構体であって、その形状の決定を、外側面板の形状を一定にして行う方法であって、コンピュータを用いて、前記鉄道車両用構体を有限な要素に分割し、前記鉄道車両用構体には一定の力が外部又は内部から作用することを条件として前記各要素における歪量を算出し、その歪量と歪量から計算される応力の積の総和が最小となるように、前記内側面板について構体厚方向の位置を変化させることによってその内側面板と前記外側面板との間の構体厚を構体全体について変化させて行うようにしたので、外側面板や内側面板の板厚を一様に厚くしなくても、構体の強度・剛性を確保することができる。
【図面の簡単な説明】
【図１】本実施の形態の鉄道車両用構体に係り、鉄道車両用構体形状の決定方法のフローチャートである。
【図２】同じく、鉄道車両用構体形状の決定方法におけるブロック図である。
【図３】同じく、最適化された鉄道車両用構体の側構体及び屋根構体の断面図である。
【図４】同じく、初期形状の鉄道車両用構体の側構体及び屋根構体の断面図である。
【図５】同じく、図４のＨ部を示すものであって、有限の要素を仮想的に表した概念図である。
【図６】同じく、初期形状の鉄道車両用構体の側構体及び屋根構体の変位図であり、点線で原型を示し、実線で変形状態を示す。
【図７】同じく、最適化された鉄道車両用構体の側構体及び屋根構体の変位図であり、点線で原型を示し、実線で変形状態を示す。
【図８】同じく、初期形状の鉄道車両用構体の側構体及び屋根構体の最大応力を示す応力図である。
【図９】同じく、最適化された鉄道車両用構体の側構体及び屋根構体の最大応力を示す応力図である。
【図１０】鉄道車両用構体の外観斜視図である。
【図１１】中空形材の拡大断面図である。
【符号の説明】
５ 中空形材
６ 外側面板
７ 内側面板
８ 中板
１０ 鉄道車両用構体
１４ 肩
３０ コンピュータ
Ａ 構体厚
Ｅ 要素[0001]
BACKGROUND OF THE INVENTION
The present invention relates to a method for determining the shape of a railway vehicle structure, which determines the shape of a railway vehicle structure formed of a hollow shape member.
[0002]
[Prior art]
Conventionally, in order to achieve two conflicting issues of securing high rigidity and reducing weight, railcar structures have been used in which, for example, bone members are welded to flat plates, and many lightweight and highly rigid bone members are used. It was used to improve the strength and rigidity of the structure. However, such a structure for a railway vehicle has a large number of parts, increases the number of welding processes, and is expensive. Therefore, in recent years, for example, a railway vehicle structure 100 made of a hollow material shown in FIG. 10 has been used.
[0003]
As shown in FIG. 10, the railway vehicle structure 100 includes a side structure 101 that forms left and right surfaces with respect to the longitudinal direction, a wife structure 102 that forms surfaces that close both ends with respect to the vehicle body longitudinal direction, and a roof. Are formed by welding thin hollow members 105 each having a predetermined width. For example, as shown in FIG. 11, the hollow shape member 105 is formed by extrusion molding so that the two face plates 106 and 107 are connected by the intermediate plate 108, and the bone member can be omitted. It is possible to reduce the number of parts and the number of welding processes.
[0004]
The hollow shape member 105 is designed with care so as to ensure the strength and rigidity of the structure and at the same time reduce the weight. That is, generally, when the railway vehicle structure 100 is constituted by the hollow shape member 105, the thickness of the structure (hereinafter referred to as “structure thickness”) A, the plate thicknesses B and C of the face plate, the arrangement of the intermediate plate, and the plate Although the thickness D is a design parameter, a uniform structure thickness is adopted for the structure thickness A from the viewpoint of maximizing the cabin space. In the examination of structure strength and rigidity, the two face plates 106, Correspondingly, the plate thicknesses B and C of 107 are changed. The joint structure 109 shown in FIG. 10 for connecting to the other railway vehicle structure 100 is fixed to the end structure 102 of the railway vehicle structure 100 configured by the hollow shape member 105, and a plurality of railway structures is provided. A railway vehicle is formed by connecting the vehicle structure 100 with a connector 109.
[0005]
[Problems to be solved by the invention]
However, the conventional railcar structure 100 has the thicknesses B and B of the face plates 106 and 107 with respect to the vertical load due to gravity and the like and the longitudinal load acting on the attachment portion of the coupler 109 when the railcar curves. It is relatively easy to change C and cope with the load, and a certain amount of weight can be reduced. On the other hand, a force is applied in the cross-sectional direction of the vehicle body against the airtight load. Only by changing the plate thicknesses B and C of 107, there is a problem that the strength and rigidity of the structure cannot be secured and the weight can not be sufficiently realized.
[0006]
For example, when a railway vehicle enters the tunnel entrance, the air pressure changes spatially in the tunnel space formed by the tunnel inner surface and the railcar outer surface. When the railway vehicle passes through the space where the air pressure changes, each railcar structure 100 has airtightness in the cabin space, so that the internal air pressure becomes higher or lower than the air pressure in the tunnel. As a result, a force in the circumferential direction of the structure is received, and a bending moment with the longitudinal direction as the rotation axis acts. Therefore, stress is repeatedly generated in each part of the railway vehicle structure 100 that has entered the tunnel due to the force and bending moment in the circumferential direction of the structure, resulting in deformation that undulates in the cross-section direction of the structure.
[0007]
Under such circumstances, the thicknesses B and C of the face plates 106 and 107 are examined so that the railcar structure 100 is not repeatedly deformed and fatigued, but only the thicknesses B and C of the face plates 106 and 107 are changed. However, it has been difficult to reduce the deformation of the structure while reducing the weight.
[0008]
Therefore, in the railway vehicle structure 100 that ensures airtightness, there is a need to reduce the weight by making the structure thickness A appropriate for each part in accordance with the force in the circumferential direction of the structure and the bending moment caused by the airtight load. Depending on the type of railway vehicle, the outline of the car body differs, and the time allowed for development, etc. It was considered difficult and was not done in actual vehicle design.
[0009]
Therefore, the present invention provides a method for determining the shape of a structure for a railway vehicle that can ensure the strength and rigidity of the structure without uniformly increasing the thickness of the outer side plate or the inner side plate in order to solve such a problem. Objective.
[0010]
[Means for Solving the Problems]
The method of determining the shape of a railway vehicle structure according to the invention is to determine the shape of a railway vehicle structure using a hollow member formed by an outer side plate, an inner side plate, and an intermediate plate, while keeping the shape of the outer side plate constant. A method of dividing the structure of the railway vehicle into finite elements by using a computer, and subjecting the railway vehicle structure to a certain force from the outside or the inside. Calculating the amount, and changing the position of the inner side plate in the structure thickness direction with respect to the inner side plate so that the total sum of the products of the strain and the stress calculated from the strain amount is minimized . The shape of the structure for a rail vehicle is determined by changing the structure thickness between the entire structures.
[0011]
Further, in the method for determining the shape of a railway vehicle structure according to the present invention, when determining the shape of the inner side plate, the cross-sectional area of the structure for the rail vehicle surrounded by the outer side plate and the inner side plate is constant. It is characterized as a condition .
[0012]
In addition, the structure for a railway vehicle uses a hollow material formed by an outer side plate, an inner side plate, and an intermediate plate, and the entire structure is divided into finite elements using a computer, and a constant force is applied. The shape of the outer face plate is calculated so that the total amount of the products of the stresses calculated from the strain amount and the strain amount is minimized by calculating the strain amount in each element on the condition that is applied from outside or inside the structure. The position of the inner side plate in the structure thickness direction is changed while keeping the value constant, and the structure thickness between the inner side plate and the outer side plate is determined for the entire structure.
[0013]
In addition, the program for determining the shape of a railway vehicle structure according to the present invention uses a computer to determine the shape of the structure for a railway vehicle using a hollow member formed by an outer side plate, an inner side plate, and an intermediate plate. The railway vehicle structure is divided into finite elements, and the amount of distortion in each element is calculated on the condition that a certain force acts on the railcar structure from the outside or the inside. The inner side plate and the outer side plate by changing the position of the inner side plate in the thickness direction of the inner side plate while keeping the shape of the outer side plate constant so that the sum of the products of stress calculated from the amount of strain is minimized. The shape of the railway vehicle structure is determined by changing the thickness of the structure between the entire structures.
[0014]
That is, in the railway vehicle structure, since the air pressure outside the structure and the air pressure inside the structure act on the outer side plate and the inner side plate, when determining the shape of the structure for the rail vehicle, a constant force is applied to the structure for the rail vehicle. It is conditional on acting from the inside. Then, the railway vehicle structure is divided into finite elements, the amount of strain and the product of the stress calculated from the amount of strain are calculated for each element, and the sum is obtained. The smaller the sum of the stress of each element and the product of the stresses calculated from the amount of distortion, the more the strain is distributed throughout the railway vehicle structure and the less concentrated stress is generated in the structure. The shape of each element is changed so that the total sum of the stresses calculated from the amount of strain and the amount of strain is minimized, and the structure thickness of the structure for railway vehicles is changed in each part according to the amount of strain, and the structure for railway vehicles Determine the shape. Therefore, according to the method for determining a structure for a railway vehicle according to the present invention, the strength and rigidity of the structure can be ensured without uniformly increasing the thickness of the outer face plate and the inner face plate.
[0015]
At that time, the shape of the outer surface plate is made constant, the shape of the inner surface plate is changed, and the shape of the initial shape of the railway vehicle structure is changed. The thickness of the structure can be changed without changing the outline, and the strength and rigidity of the structure can be ensured in accordance with the outline of each railway vehicle structure.
[0016]
In addition, the shape of the initial structure for railway vehicles has been changed so that the area between the outer side plate and the inner side plate is constant, and when the shape of one element is increased, the shape of the other element is reduced. The structure formed by the outer side plate and the inner side plate does not become unnecessarily thick. Therefore, even if the strength and rigidity of the structure are secured, the weight is hardly increased and the weight can be reduced. .
[0017]
Since the thickness of the structure for a railway vehicle body optimized in this way is changed in accordance with the amount of distortion of each part of the structure, the structure of the structure can be obtained without uniformly increasing the thickness of the outer side plate and the inner side plate. Strength and rigidity can be ensured. Specifically, for example, when a bent part of a railway vehicle structure receives an external force, the outer side plate receives a tensile load and the inner side plate receives a compressive load. However, by optimizing with the above-mentioned method for determining the shape of a structure for a railway vehicle, only the structure thickness of the bent portion is increased so that it can withstand tensile loads and compressive loads. Improvement and weight reduction can be sufficiently realized.
[0018]
DETAILED DESCRIPTION OF THE INVENTION
Next, an embodiment of a method for determining a structure for a railway vehicle according to the present invention will be described with reference to the drawings. FIG. 3 shows a cross-sectional view of the side structure 1 and the roof structure 3 of the optimized railway vehicle structure 10. FIG. 4 shows a cross-sectional view of the side structure 21 and the roof structure 23 of the railway vehicle structure 20 having an initial shape.
The railcar structure 10 of the present embodiment shown in FIG. 3 is configured by connecting the side structure 1 and the roof structure 3 to a hollow shape member 5 (see FIG. 11) made of an aluminum alloy, as in the prior art. However, the structure thickness A of the side structure 1 and the roof structure 3, that is, the thickness of the structure formed by the outer side plate 6 and the inner side plate 7 (see FIG. 11) is changed in each part of the structure. It is different from the conventional one. Therefore, here, a description of a specific configuration of the railway vehicle structure 10 is omitted, and the shape is changed by changing the structure thickness A (see FIG. 11) of the railway vehicle structure 20 as shown in FIG. A method for determining the shape of a railway vehicle structure will be mainly described.
[0019]
FIG. 2 is a block diagram of a method for determining the shape of a railway vehicle structure.
A computer 30 is used in the method for determining the structure of a railway vehicle. In the computer 30, an input / output device 32, a storage device 33, and the like are connected to a CPU 31 that performs various calculations and controls. The input / output device 32 is used to input data and the like and output calculation results and the like. The storage device 33 stores information input from the input / output device 32, calculation results calculated by the CPU, programs, and the like.
[0020]
Here, in the railway vehicle structure 10, in terms of strain and stress generated by the initial shape (structure thickness A given as an initial value) and boundary conditions (load load, constraint conditions) given to the region, Consider the following formula called average compliance (Φ). ε is a strain, D is a stress-strain relationship, and Ω is a region to be studied.
[0021]
[Expression 1]

[0022]
In the present embodiment, the state minimized under the constraint conditions (volume, partial structure thickness fixation, structure thickness minimum value, etc.) to which the average compliance is given is optimal. Regarding the minimization of the average compliance, for example, it is published in “Area Optimization Analysis in Linear Elasticity Problems” published on pages 144-150 of the Japan Society of Mechanical Engineers (A) Volume 60, 578 (1994-10). In this embodiment, the structure of the railway vehicle structure is optimized by using a program that performs analysis based on “region optimization analysis in linear elasticity problem”. This program is stored in the storage device 33 of the computer 30.
[0023]
In “Regional Optimization Analysis in Linear Elasticity Problems”, the domain optimization problem with the shape of the linear elastic body as a design variable is formulated as a continuum, and the optimization theory of the distribution system is applied. We approach the domain optimization problem based on the derived governing equation of domain variation. The numerical analysis method is formulated as a method for solving the governing equation, and a force method is proposed as one of the methods. The force method is practical in that a finite element method or the like can be used to solve the domain variation governing equation by replacing it with a boundary value problem of a linear elasticity problem. The shape gradient function appearing in the governing equation can also be analyzed using a finite element method or the like.
Therefore, “Regional Optimization Analysis in Linear Elasticity Problem” formulates the minimization problem of average compliance, clarifies the shape gradient function calculated based on the optimality criterion and the optimization criterion, and The force method using the gradient function is applied to the domain problem of linear elastic bodies.
[0024]
When dealing with the region minimization problem of linear elastic continuum, average compliance is selected as the objective functional in the “region optimization analysis in linear elastic problem”. In this case, as will be described later, the region optimization problem becomes a self-adjoint problem, and the shape gradient function can be evaluated only by a displacement that is a solution of linear elastic deformation. In this sense, average compliance can be considered as a mechanically simple objective functional.
[0025]
The average compliance minimization problem is formulated as follows.
The relationship between the external force acting on the linear continuum and the object force is given by Equation 4, and the relationship such as gravity that displaces the linear continuum is given by Equation 5. Here, Ω represents a region, u represents a displacement of a linear continuum, f represents an object force, h represents a forced displacement, and P represents a surface force. The weak form or variational form for the boundary value problem is expressed as in Equation 2.
[0026]
[Expression 2]

[0027]
However, the bilinear form a (υ, ω) and the primary forms l (ω), l _h (ω) are defined as in the equations 3 to 5.
[0028]
[Equation 3]

[Expression 4]

[Equation 5]

[0029]
Further, the Hooke stiffness CεL∽ (Ω; R ⁿ⁴ ) assumes the following symmetry and positive definiteness as in the following equation. Here, L∽ (Ω; R ⁿ ) represents a bounded integrable Lebesgue function space.
[0030]
[Formula 6]

[0031]
Assuming that the distribution functions C, f, h, and P are uniquely determined with respect to the region variation, CεC ¹ (D; R ⁿ⁴ ), When f, h, PεC ¹ (D; R ⁿ ) and the upper limit value MεR ₊ for the region size are given, the average compliance is expressed as in Equation 7.
[0032]
[Expression 7]

[0033]
And when calculating | requiring area | region (omega | ohm _{3) in} which the average compliance represented by several 7 becomes the minimum, it is necessary to satisfy | fill the equation of state shown in several 8, and the mass constraint shown in several 9.
[0034]
[Equation 8]

[Equation 9]

[0035]
Next, the optimality criterion is obtained.
The optimality criterion is derived by applying the Lagrange constant. When ω is used for the Lagrange constant of the equation (8) and Λ is used for the Lagrange constant of the inequality (9), the problem of minimizing the average compliance is the Lagrange function shown in equation (10). Can be rewritten as
[0036]
[Expression 10]

[0037]
The derivative with respect to the region variation of the Lagrange function can be expressed as shown in Equation 11.
[0038]
[Expression 11]

[0039]
Here, if C, f, h, and P are unique with respect to the region variation, l _G (V) is given by the linear form of the velocity field V having the vector function G as a coefficient function as shown in Expression 12. become.
[0040]
[Expression 12]

[0041]
G is a vector function that gives a sensitivity coefficient of an objective functional with respect to a velocity field that gives a region variation, and is called a shape gradient function. C, f, h are spatially fixed, h = oinD, material covariant P + P _k υ When G is specifically obtained assuming that _n = o (that is, gravity and physical properties do not change depending on the place), the following equation 13 is obtained.
[0042]
[Formula 13]

[0043]
Here, the stopping condition of the Lagrange function L is expressed by Equations 14 to 18 based on Equation 11.
[0044]
[Expression 14]

[Expression 15]

[Expression 16]

[Expression 17]

[Expression 18]

[0045]
Looking at Equations 14 to 18, Equation 14 is the governing equation for v that matches the equation of state υ = u−h shown in Equation 2. Equation 15 is the governing equation for ω. When the two are compared, the relationship shown in Equation 19 is obtained.
[0046]
[Equation 19]

[0047]
Then, in order to simplify the calculation, the object force is not considered, and when Equation 19 is applied to Equation 13, the relationship of Equation 20 is obtained.
[0048]
[Expression 20]

[0049]
Thus, since the derivative of the Lagrange function is given in the primary form of the velocity field V having the shape gradient function G as a coefficient, the force method using the shape gradient function G can be applied. In the force method, V ^(k) representing region variation when considering k-th region variation from the initial region Ω is analyzed based on the governing equation shown in Equation 21.
[0050]
[Expression 21]

[0051]
The region variation V ^(k) determined by the governing equation shown in Equation 21 decreases the Lagrange function L. That is, the governing equation of region variation analysis shown in Equation 21 indicates that the velocity field V that gives region variation is analyzed as a displacement distribution when a force -G is applied to the boundary or region.
[0052]
Next, a method for determining the shape of a railway vehicle structure according to the present embodiment will be described with reference to the drawings. FIG. 1 is a flowchart of a method for determining the shape of a railway vehicle structure, and FIG. 5 is a conceptual diagram showing the H part of FIG. 4 and virtually representing finite elements.
The method for determining the structure for a railway vehicle is performed by the CPU 31 of the computer 30 reading a program from the storage means 33 and executing the processing of the flowchart shown in FIG. Therefore, in the method for determining the shape of a structure for a railway vehicle, first, in step 1 of FIG. 1 (hereinafter referred to as “S1”), an initial shape analysis model (finite element method) is input from the input / output device 32 and the storage device 33. To remember.
[0053]
Specifically, as shown in FIG. 5, the entire railway vehicle structure 20 is divided into finite elements E, and coordinate data is attached to the nodes ● of each element E, for example, four nodes ● (i˜ Input the element information of the finite element method to the effect of l). Then, the initial value of the structure thickness A (see FIG. 11) composed of the outer face plate 6 and the inner face plate 7 is set to 50 mm, and the Young's modulus and Poisson's ratio of the aluminum alloy are input as the material characteristics of the railway vehicle structure 20. . Then, a constraint condition and a load condition are input as boundary conditions used when performing strength analysis or the like. As constraint conditions, it is input that the portion 25 corresponding to the underframe side beam shown in FIG. 4 is fixed and that a symmetry condition is added to the center line M of the railway vehicle structure 20. Here, the symmetry condition is added in order to reduce the calculation amount and the calculation time. Further, as a load condition, it is input that an equally distributed load S is applied to the outside of the railway vehicle structure 20 assuming an airtight load.
[0054]
Next, in S2, strength analysis of the railway vehicle structure 20 is performed. The strength analysis is performed by the CPU 31 of the computer 30 reading the initial shape analysis model stored in the storage device 33 in S1 and calculating the strain amount and the generated stress for each element E based on the model.
[0055]
Next, in S3, sensitivity analysis is performed. In the sensitivity analysis, the CPU 31 of the computer 30 obtains the shape gradient function G based on the formula 22 using the force method.
[0056]
[Expression 22]

[0057]
The shape gradient function G obtained from Equation 22 is a vector function facing the normal direction distributed on the boundary surface of each element E shown in FIG. Here, the value of the variable appearing in the equation is obtained from the analysis result of the strength analysis of S2, where f is an object force, e is an elastic tensor, u is a displacement, and Λ is a Lagrange constant.
[0058]
In S4, a convergence determination is performed. The convergence determination is made based on whether or not the sensitivity obtained by executing the sensitivity analysis is sufficiently small. If it is determined that the sensitivity is sufficiently small (S4: YES), the process is terminated. On the other hand, when it is determined that the sensitivity is not sufficiently low (S4: NO), the process proceeds to S5, and it is determined whether or not a constraint condition for shape change is input. If it is determined that the constraint condition has been input (S5: YES), the process proceeds directly to S7.
[0059]
On the other hand, when it is determined that no constraint condition has been input (S5: NO), in S6, the restriction of the shape is not permitted as a constraint condition, the constraint on the moving direction, the volume (three-dimensional problem) or the area ( The two-dimensional problem is input from the input / output device 32 and stored in the storage device 33, and then the process proceeds to S7. As a specific constraint condition, for example, the movement of the node ● located at a thickness of 40 mm from the outer face plate 6 (see FIG. 11) of the hollow shape member 5 constituting the side structure 21 and the roof structure 23 is not permitted. Input that the node of each element E (see FIG. 5) is moved only in the x direction (one-dimensionally) and that the area surrounded by the outer side plate 6 and the inner side plate 7 is the same as the initial shape. . Here, fixing the thickness of 40 mm from the outer face plate 6 (see FIG. 11) of the hollow member 5 constituting the side structure 21 and the roof structure 23 avoids the structure thickness A from being 40 mm or less. Because. In addition, the node of each element E (see FIG. 5) is moved only in the x direction (one-dimensionally) so that each element E is expanded and contracted in the structure thickness A direction so that the vehicle outline is not changed. It is to make it.
[0060]
In S7, the shape of the railway vehicle structure 20 is changed. Specifically, the CPU 31 of the computer 30 reads out the constraint condition stored in the storage device 33, applies a force to the boundary surface of each element E in proportion to the magnitude of the shape gradient function G, and the node ● (Fig. 5) is moved, and the coordinate data of the node ● stored in the storage device 33 is rewritten. As a result, the size and shape of each element E change, and the shape of the railway vehicle structure 20 changes from the initial shape. If the shape of the railway vehicle structure 20 is changed, the process returns to S3 and is repeated.
[0061]
Such a method for determining the shape of a structure for a railway vehicle operates as follows.
As shown in FIG. 4, an initial-shaped railcar structure 20 formed with a uniform structure thickness A is divided into finite elements E, coordinate data of each node ●, element information of the finite element method, aluminum alloy An initial shape analysis model such as Young's modulus and Poisson's ratio is input to obtain strength analysis, and a shape gradient function G is obtained based on the initial shape analysis model and the strength analysis result (S1 to S3).
[0062]
When the sensitivity is not sufficiently low in the convergence determination, that is, when the shape gradient function G has a steep gradient, the shape of the railway vehicle structure 20 is changed based on the constraint condition (S4: NO, S5: YES). , S7).
Specifically, for example, when the shape gradient function G is locally large, the 40 mm node ● is not moved from the outside of the side structure 21 and the roof structure 23 with respect to the portion where the shape gradient function G is large. Based on constraints such as the movement direction of ● being limited to the x direction, the node ● of the element E in the portion within 10 mm from the inside of the side structure 21 and the roof structure 23 is moved inward, and the element E Reduce the size of to increase the number of elements. Further, since there is a constraint that the area between the outer side plate 6 and the inner side plate 7 is constant, the element E in the portion within 10 mm from the inner side of the side structure 21 and the roof structure 23 with respect to the portion where the shape gradient function G is small. Is moved outward, the size of element E is increased, and the number of elements is reduced. When the division method of the element E is changed in this way, the coordinate data of the moved node ● is rewritten. As a result, the structure thickness A is increased in the portion where the number of elements is increased, and the structure thickness A is decreased in the portion where the number of elements is decreased, so that the shape of the initial structure 20 for the railway vehicle is changed. If the shape of the railway vehicle structure 20 is changed, the process returns to S3 and is repeated. These series of processes are automatically performed until it is determined that the sensitivity is sufficiently low in the convergence determination.
[0063]
When it is determined that the sensitivity is sufficiently low in the convergence determination, that is, when the gradient of the shape gradient function G is small, the process ends (S4: YES), and the optimization is performed as shown in FIG. The railway vehicle structure 10 thus produced is output to the input / output device 32. That is, in the railway vehicle structure 20 shown in FIG. 4, for example, an external pressure is applied to a connection portion between the side structure 21 and the roof structure 23, that is, a bent portion (hereinafter referred to as “shoulder portion”) 24 of the structure. In this case, a tensile stress acts on the outer side plate 6 and a compressive stress is generated on the inner side plate 7, so that fatigue breakdown is likely to occur. However, by executing the processing shown in FIG. The 20 shoulder portions 24 are thickened like the shoulder portions 14 of the railway vehicle structure 10 shown in FIG. On the other hand, in the railway vehicle structure 10 shown in FIG. 3, the portions 16 and 17 corresponding to both ends of the shoulder portion 34 are made thinner than the railway vehicle structure 20 shown in FIG.
[0064]
By the way, in order to confirm the characteristics relating to the displacement and stress of the optimized railway vehicle structure 10, the inventor has the initial shape railway vehicle structure 20 shown in FIG. 4 and the optimized railway vehicle shown in FIG. 3. The displacement amount of the structural body 10 was compared. FIG. 6 is a displacement diagram of the railcar structure 20 having an initial shape, in which a prototype is shown by a dotted line and a deformed state is shown by a solid line. FIG. 7 is a displacement diagram of the optimized structure 20 for a railway vehicle, in which a prototype is shown by a dotted line and a deformed state is shown by a solid line.
[0065]
In this experiment, a 98 kPa equally distributed load was applied to the outside of the railway vehicle structures 10 and 20.
As a result, in the railcar structure 20 having the initial shape, as shown in FIG. 6, the side structure 21 is hardly deformed, and the roof structure 23 is greatly deformed from the shoulder portion 24 of the railcar structure 20. In particular, the deformation is large at the center of the roof structure 23, and the displacement amount T1 is about 3.27 mm. On the other hand, in the optimized railway vehicle structure 10, as shown in FIG. 7, the entire side structure 1 and the roof structure 3 are deformed, and the distortion is distributed to the side structure 1 and the roof structure 3. Yes. Therefore, in the center part of the roof structure 3, the displacement amount T2 is about 1.48 mm.
Therefore, when the displacement at the center of the roof structures 3 and 23 of the optimized railway vehicle structure 10 and the initial shape of the railway vehicle structure 20 is compared, the optimized railway vehicle structure 10 is It has been found that the displacement is reduced by about 55% from the vehicle structure 20.
[0066]
The inventor also examined the stress distribution in the initial shape of the railcar structure 20 and the optimized railcar structure 10. FIG. 8 is a stress diagram showing the maximum stresses of the side structure 21 and the roof structure 23 of the railcar structure 20 in the initial shape, and FIG. 9 is the side structure 1 and the roof structure of the optimized structure 10 for a railcar. 3 is a stress diagram showing a maximum stress of 3. FIG.
[0067]
In this experiment, a 98 kPa equally distributed load was applied to the outside of the railway vehicle structures 10 and 20.
As a result, as shown in FIG. 8, in the initial configuration of the railway vehicle structure 20, the stress generated in the inner side plate 7 is lower than the stress generated in the outer side plate 6 in the shoulder portion 24. . As described above, when the stress generated between the outer side plate 6 and the inner side plate 7 is imbalanced, there is a problem that the stress concentrates on the inner side plate 7 having a low stress, and the inner side plate 7 is easily damaged by fatigue. On the other hand, in the optimized railway vehicle structure 10, as shown in FIG. 9, the stress generated in the outer side plate 6 and the inner side plate 7 is almost uniform in the shoulder portion 14. The problem of stress concentration on any one of 7 is avoided. The optimized railway vehicle structure 10 is substantially the same as the side structure 21 of the initial shape railcar structure 20 even if the side structure 1 is thinner than the side structure 21 of the initial shape railcar structure 20. The same stress is generated.
Therefore, the optimized railway vehicle structure 10 improves the strength and rigidity by increasing the thickness of the portion with a large load load, while improving the strength and rigidity as compared with the initial shape of the rail vehicle structure 20. It can be seen that because the thickness is reduced while maintaining the strength and rigidity, an increase in the weight of the structure can be suppressed while improving the strength and rigidity of the structure.
[0068]
Therefore, the railway vehicle structure 10 according to the present embodiment divides the railway vehicle structure 20 into finite elements E on the condition that a certain stress acts on the initial shape of the railway vehicle structure 20 from the outside and the inside. Then, the shape gradient function G is calculated so that the calculation result of the shape gradient function G converges, that is, for each element, the product of the strain and the stress calculated from the strain amount is calculated, and the sum is small. Since the shape of the railway vehicle structure 20 is changed, the distortion generated in the structure is dispersed throughout the structure, and the thicknesses B and C (see FIG. 11) of the outer side plate 6 and the inner side plate 7 are uniformly increased. Even without this, the strength and rigidity of the structure can be secured.
[0069]
At that time, the shape of the outer side plate 6 is made constant, the shape of the inner side plate 7 is changed, and the shape of the initial shape of the railway vehicle structure 20 is changed. The structure thickness A is changed without changing the outline of the vehicle structure 20, and the strength and rigidity of the structure can be ensured according to the outline of each of the railway vehicle structures 20.
[0070]
In addition, the shape of the initial shape of the railcar structure 20 is changed so that the area between the outer side plate 6 and the inner side plate 7 is constant, and when the shape of one element E is increased, another element E Since the structure thickness A formed by the outer face plate 6 and the inner face plate 7 does not become unnecessarily thick, the weight of the structure is almost increased even if the strength and rigidity of the whole structure are ensured. Therefore, weight reduction can be realized.
[0071]
In the optimized structure 10 for a railway vehicle, since the structure thickness A of each part of the structure is changed according to the amount of distortion of each part of the structure, the thickness of the outer side plate 6 and the inner side plate 7 is uniformly increased. Without it, the strength and rigidity of the structure can be secured.
[0072]
Further, in the optimized structure 10 for a railway vehicle, for example, the shoulder portion 14 receives a tensile load on the outer side plate 6 and a compressive load on the inner side plate 7, but is thick enough to handle these loads. Since the structure thickness A of the necessary part is increased by a necessary amount, it is possible to sufficiently ensure the strength and rigidity of the structure and reduce the weight. In addition, since the parts 16 and 17 connected to the shoulder 24 are made thin with sufficient strength and rigidity, the weight of the structure is hardly increased and the weight is reduced even if the strength and rigidity of the entire structure is secured. can do.
[0073]
In addition, this invention is not necessarily limited to the thing of embodiment, It cannot be overemphasized that various changes are possible in the range which does not deviate from the meaning.
[0074]
【The invention's effect】
Therefore, the present invention is a railway vehicle structure using a hollow member formed of an outer face plate, an inner face plate, and an intermediate plate, and the shape is determined by a method in which the shape of the outer face plate is made constant. Then, using a computer, the railway vehicle structure is divided into finite elements, and the amount of distortion in each element is calculated on the condition that a constant force acts on the railway vehicle structure from the outside or the inside. The structure between the inner side plate and the outer side plate is changed by changing the position of the inner side plate in the thickness direction of the structure so that the total sum of the products of the strain and the stress calculated from the strain amount is minimized. Since the thickness is changed for the entire structure, the strength and rigidity of the structure can be ensured without uniformly increasing the thickness of the outer face plate and the inner face plate.
[Brief description of the drawings]
FIG. 1 is a flowchart of a method for determining the shape of a railway vehicle structure according to the railway vehicle structure of the present embodiment.
FIG. 2 is a block diagram of a method for determining the shape of a railway vehicle structure.
FIG. 3 is a cross-sectional view of a side structure and a roof structure of an optimized railway vehicle structure, similarly;
FIG. 4 is a cross-sectional view of the side structure and the roof structure of the railway vehicle structure having the initial shape.
5 is a conceptual diagram showing the H part of FIG. 4 and virtually representing a finite element. FIG.
FIG. 6 is also a displacement diagram of the side structure and the roof structure of the railway vehicle structure having an initial shape, showing a prototype with a dotted line and a deformed state with a solid line.
FIG. 7 is also a displacement diagram of the side structure and the roof structure of the optimized railway vehicle structure, in which a prototype is shown by a dotted line and a deformed state is shown by a solid line.
FIG. 8 is a stress diagram showing the maximum stress of the side structure and the roof structure of the railway vehicle structure having the initial shape.
FIG. 9 is a stress diagram showing the maximum stress of the side structure and the roof structure of the optimized railway vehicle structure, similarly;
FIG. 10 is an external perspective view of a railway vehicle structure.
FIG. 11 is an enlarged cross-sectional view of a hollow shape member.
[Explanation of symbols]
5 Hollow material 6 Outer side plate 7 Inner side plate 8 Middle plate 10 Railcar structure 14 Shoulder 30 Computer A Structure thickness E Element

Claims (3)

In the method for determining the shape of a railway vehicle structure in which the shape of the structure for a railway vehicle using a hollow profile formed by the outer side plate, the inner side plate, and the middle plate is determined, with the shape of the outer side plate being constant
Using a computer, the railway vehicle structure is divided into finite elements, and the amount of distortion in each element is calculated on the condition that a certain force acts on the railway vehicle structure from the outside or the inside. The structure thickness between the inner surface plate and the outer surface plate is changed by changing the position of the inner surface plate in the structure thickness direction so that the total sum of the products of the strain and the stress calculated from the strain amount is minimized. A method for determining the shape of a railway vehicle structure, wherein the shape of the structure for a rail vehicle is determined by changing the whole. A method for determining the shape of a railway vehicle structure according to claim 1,
A method for determining a shape of a railway vehicle structure, characterized in that, when the shape of the inner side plate is determined, a cross-sectional area of the structure for a rail vehicle surrounded by the outer side plate and the inner side plate is constant. In a program for determining the shape of a railway vehicle structure using a computer, the shape of the structure for a railway vehicle using a hollow shape member formed by an outer side plate, an inner side plate, and an intermediate plate is provided.
The railway vehicle structure is divided into finite elements, and the amount of distortion in each element is calculated on the condition that a certain force acts on the railway vehicle structure from the outside or the inside. By changing the position of the inner side plate in the thickness direction of the inner side plate while keeping the shape of the outer side plate constant so that the sum of the products of stress calculated from A program for determining the shape of a railway vehicle structure, wherein the shape of the railway vehicle structure is determined by changing the thickness of the structure for the entire structure.

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