JP2698029B2 - A method for obtaining stress distribution from temperature change patterns on the surface of an elastic body - Google Patents
A method for obtaining stress distribution from temperature change patterns on the surface of an elastic bodyInfo
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- JP2698029B2 JP2698029B2 JP5239392A JP23939293A JP2698029B2 JP 2698029 B2 JP2698029 B2 JP 2698029B2 JP 5239392 A JP5239392 A JP 5239392A JP 23939293 A JP23939293 A JP 23939293A JP 2698029 B2 JP2698029 B2 JP 2698029B2
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- stress
- distribution
- elastic body
- temperature change
- sum
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Description
【０００１】[0001]
【産業上の利用分野】本発明は、弾性体表面の温度変化
パターンから応力分布を求める方法に関し、特に、熱弾
性効果による弾性体表面の温度変化パターンデータと数
値応力解析による解析データとから弾性体の応力分布を
求める方法に関する。BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for obtaining a stress distribution from a temperature change pattern on the surface of an elastic body. The present invention relates to a method for determining a stress distribution of a body.
【０００２】[0002]
【従来の技術】弾性体の任意の１点における応力は、
（ｘ，ｙ，ｚ）直交座標で表して、一般に６つの成分σ
x ，σy ，σz ，τxy，τyz，τzxで表される。この
中、σx ，σy ，σz はそれぞれｘ，ｙ，ｚ軸に垂直な
平面に作用する垂直応力成分、τxyはｘ＝一定の面でｙ
方向に作用、及び、ｙ＝一定の面でｘ方向に作用する剪
断応力であり、τyz，τzxも添字に関して同じ定義に従
う剪断応力である。また、その点に関して適当な座標系
を選ぶと、剪断応力成分は全て消え、垂直応力成分のみ
が存在することになり、その垂直応力成分は主応力成分
σ1 ，σ2 ，σ3 と呼ばれる。2. Description of the Related Art The stress at any one point of an elastic body is as follows.
Expressed in (x, y, z) rectangular coordinates, generally six components σ
x , σ y , σ z , τ xy , τ yz , τ zx . Among them, σ x , σ y , and σ z are vertical stress components acting on planes perpendicular to the x, y, and z axes, respectively, and τ xy is y in a x = constant plane.
Acting in the direction and y = shear stress acting in the x direction on a constant plane, and τ yz and τ zx are also shear stresses according to the same definition with respect to the subscripts. If an appropriate coordinate system is selected for that point, all the shear stress components disappear and only the normal stress component exists, and the normal stress components are called main stress components σ 1 , σ 2 , and σ 3 .
【０００３】ところで、弾性体に断熱的に応力変化を与
えるとそれに比例して温度変化が生じることが、熱弾性
効果（ｔｈｅｒｍｏｅｌａｓｔｉｃ ｅｆｆｅｃｔ）と
して１９世紀からＷｅｂｅｒ，Ｋｅｌｖｉｎ等によって
知られていた。この熱弾性効果により生じる応力印加前
後の温度差をΔＴとすると、 ΔＴ＝−ＫＴ（σ1 ＋σ2 ＋σ3 ） の関係がある。ここで、Ｋは材料に固有の定数で熱弾性
定数、Ｔは絶対温度である。なお、ここで、主応力和
（σ1 ＋σ2 ＋σ3 ）は第１次応力不変量であり、座標
軸（ｘ，ｙ，ｚ）の取り方に無関係に（σx ＋σy ＋σ
z ）に等しいことが弾性論によって証明されている。Δ
Ｔが主応力和に比例するのは、弾性体の体積の変化が第
１次応力不変量によって決まり、剪断応力成分τxy，τ
yz，τzxによっては弾性体の体積変化は起きないからで
ある。It has been known from the 19th century by Weber, Kelvin, and the like, as a thermoelastic effect, that a temperature change occurs in proportion to an adiabatic stress change applied to an elastic body. Assuming that a temperature difference before and after stress application caused by the thermoelastic effect is ΔT, there is a relationship of ΔT = −KT (σ 1 + σ 2 + σ 3 ). Here, K is a constant unique to the material and a thermoelastic constant, and T is an absolute temperature. Here, the sum of the principal stresses (σ 1 + σ 2 + σ 3 ) is a primary stress invariant and is (σ x + σ y + σ irrespective of how to take the coordinate axes (x, y, z)).
z ) is proved by the theory of elasticity. Δ
T is proportional to the sum of the principal stresses because the change in volume of the elastic body is determined by the first-order stress invariant, and the shear stress components τ xy , τ
This is because the volume change of the elastic body does not occur depending on yz and τ zx .
【０００４】本出願人は、この熱弾性効果を利用して、
弾性体に圧縮・引っ張り荷重を繰り返し加え、それに伴
う弾性体表面の温度変化パターンを赤外線カメラで検出
することにより、簡単に応力分布を測定する方法を特公
昭６２−１２０４〜５号、同６３−７３３３号等におい
て提案している。[0004] The present applicant utilizes this thermoelastic effect,
A method of easily measuring a stress distribution by repeatedly applying a compressive / tensile load to an elastic body and detecting a temperature change pattern of the surface of the elastic body with an infrared camera is disclosed in JP-B-62-1204-5 and JP-B-63-12063. No. 7333 and the like.
【０００５】一方、弾性体の応力分布を数値解析的に求
める方法として、有限要素法、境界要素法、差分法等が
知られている。これらは、実物と同じ形状のモデルに弾
性定数と加える外力を境界条件として与え、近似的に弾
性体内部及びその表面の応力分布等を求める数値解析的
手法である。On the other hand, a finite element method, a boundary element method, a difference method and the like are known as methods for obtaining the stress distribution of an elastic body by numerical analysis. These are numerical analysis techniques that give an elastic constant and an external force to be applied to a model having the same shape as the actual product as boundary conditions, and approximately determine the stress distribution and the like inside the elastic body and its surface.
【０００６】[0006]
【発明が解決しようとする課題】上記のように、熱弾性
効果による弾性体表面の温度変化パターンは、主応力和
（σ1 ＋σ2 ＋σ3 ）の分布に比例するが、この温度変
化パターンデータからは、応力成分σx ，σy ，σz ，
τxy，τyz，τzxそれぞれを分離して知ることはできな
い。一方、有限要素法等の数値応力解析法においては、
境界条件を適正に与えることが容易ではなく、そのため
得られた結果が実物の応力分布に対応するかは必ずしも
確実ではない。As described above, the temperature change pattern of the elastic body surface due to the thermoelastic effect is proportional to the distribution of the sum of the principal stresses (σ 1 + σ 2 + σ 3 ). From the stress components σ x , σ y , σ z ,
τ xy , τ yz , and τ zx cannot be separately known. On the other hand, in numerical stress analysis methods such as the finite element method,
It is not easy to give the boundary conditions properly, and it is not always certain that the obtained result corresponds to the actual stress distribution.
【０００７】本発明はこのような従来技術の問題点に鑑
みてなされたものであり、その目的は、熱弾性効果によ
る弾性体表面の温度変化パターンデータと数値応力解析
による解析データを組み合わせることにより、弾性体の
個々の応力成分を含めた応力分布を求める簡単な方法を
提供することである。The present invention has been made in view of such problems of the prior art, and an object of the present invention is to combine temperature change pattern data of an elastic body surface due to a thermoelastic effect with analysis data obtained by numerical stress analysis. Another object of the present invention is to provide a simple method for obtaining a stress distribution including individual stress components of an elastic body.
【０００８】[0008]
【課題を解決するための手段】上記目的を達成する本発
明の弾性体表面の温度変化パターンから応力分布を求め
る方法は、弾性体実物に断熱的に応力変化を与えて熱弾
性効果による実物表面の温度変化パターンを検出し、そ
の温度変化パターンから実物表面の内点における主応力
和を求め、また、その実物と同形状の構造体モデルの境
界に複数の自由接点を定め、特定の１つの自由接点に単
位外力を印加した時の実物表面の内点における主応力和
を数値応力解析により求め、次いで、重ね合わせ原理と
最小自乗法により、実測主応力和分布に最も近い主応力
和分布を与える各自由接点にかかる外力分布を求め、得
られた外力分布から数値応力解析により実物の任意の点
にかかる応力成分を求めることを特徴とする方法であ
る。In order to achieve the above object, a method of obtaining a stress distribution from a temperature change pattern on an elastic body surface according to the present invention is a method for adiabatically applying a stress change to an elastic body by adiabatic thermal elasticity effect. The temperature change pattern is detected, the principal stress sum at the inner point of the actual surface is determined from the temperature change pattern, and a plurality of free contact points are determined at the boundary of the structural model having the same shape as the actual object, and a specific one The principal stress sum at the inner point of the actual surface when a unit external force is applied to the free contact point is obtained by numerical stress analysis, and then the principal stress sum distribution closest to the measured principal stress sum distribution is calculated by the superposition principle and the least square method. The method is characterized in that an external force distribution applied to each given free contact point is obtained, and a stress component applied to an arbitrary point on the actual object is obtained from the obtained external force distribution by numerical stress analysis.
【０００９】[0009]
【作用】本発明においては、熱弾性効果による弾性体表
面の温度変化パターンデータから求めた実測主応力和分
布に最も近い主応力和分布を与える各自由接点にかかる
外力分布を求め、得られた外力分布から数値応力解析に
より実物の任意の点にかかる応力成分を求めるので、実
物表面及び内部における応力成分の分布を簡単な方法で
精度よく求めることができる。In the present invention, the external force distribution applied to each free contact which gives the main stress sum distribution closest to the measured main stress distribution obtained from the temperature change pattern data of the elastic body surface due to the thermoelastic effect was obtained and obtained. Since the stress component applied to an arbitrary point on the actual object is obtained from the external force distribution by numerical stress analysis, the distribution of the stress component on the surface and inside of the actual object can be accurately obtained by a simple method.
【００１０】なお、異なる外力によって同一点に同じ主
応力和が生じる平滑な丸棒の引っ張りの問題と捩じりと
引っ張りを受ける問題等は、主応力和のみの情報からは
原理的に応力成分の分離が不可能であるが、このような
問題は実用上の重要性は低く、一般に実用上重要な問題
ではこのような不都合は生じず、本発明によって解決す
ることができる。[0010] The problem of pulling a smooth round bar and the problem of being subject to torsion and pulling, in which the same principal stress sum is generated at the same point due to different external forces, is due to the fact that the stress component is in principle based on the information of the principal stress sum alone. However, such a problem is of low practical importance, and generally, such a problem does not cause such inconvenience, and can be solved by the present invention.
【００１１】[0011]
【実施例】以下、本発明の原理を説明するが、前提とし
て、弾性体実物に所定の応力変化を与えた時の温度変化
パターンが、本出願人による特公昭６２−１２０４〜５
号、同６３−７３３３号等の熱弾性効果を利用した方法
により検出され、そのパターンデータから弾性体実物表
面における主応力和（σ1 ＋σ2 ＋σ3 ）の分布が求め
られているものとする（なお、この主応力和（σ1 ＋σ
2 ＋σ3 ）は（σx＋σy ＋σz ）に等しい。）。ま
た、この実物に対応する形状のモデルに弾性定数を与
え、その境界に境界条件として外力を与えることによ
り、そのモデルの内部及びその表面の応力分布が有限要
素法等の数値応力解析により求まるものとする。DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS The principle of the present invention will be described below. The premise is that the temperature change pattern when a predetermined stress change is applied to an actual elastic body is determined by the applicant of the present invention.
No. 63-7333, and the distribution of the principal stress sum (σ 1 + σ 2 + σ 3 ) on the surface of the actual elastic body is determined from the pattern data. (Note that this principal stress sum (σ 1 + σ
2 + σ 3 ) is equal to (σ x + σ y + σ z ). ). By giving an elastic constant to the model of the shape corresponding to this real object and applying an external force to the boundary as a boundary condition, the stress distribution inside the model and its surface can be obtained by numerical stress analysis such as the finite element method. And
【００１２】さて、このような前提の下に、図１に模式
的に示すように、このモデル１の主応力和が求まってい
る表面を要素ｊ（ｊ＝１〜ｎ）に分割し、その要素位置
（内点）における主応力和（σ1 ＋σ2 ＋σ3 ）をZ(j)
とする。このように、実物１表面におけるZ(j)の分布が
分かった時に、実物１表面の自由接点（変位の拘束がな
い接点）ｉにかかる外力P(i)（ｉ＝１〜ｍ）を見積も
る。なお、P(i)にはその自由接点ｉにおける垂直成分と
接線成分があるが、以下の議論では、簡単のために１つ
のみとする。Under the above assumption, as shown schematically in FIG. 1, the surface of the model 1 for which the sum of the principal stresses is obtained is divided into elements j (j = 1 to n). The principal stress sum (σ 1 + σ 2 + σ 3 ) at the element position (inner point) is Z (j)
And As described above, when the distribution of Z (j) on the surface of the actual object 1 is known, the external force P (i) (i = 1 to m) applied to the free contact (contact point having no displacement) i on the actual object 1 surface is estimated. . Note that P (i) has a vertical component and a tangential component at the free contact point i, but in the following discussion, only one is provided for simplicity.
【００１３】自由接点ｉに外力P(i)＝１のみをかけた時
の要素ｊにおける主応力和（σ1 ＋σ2 ＋σ3 ）をF(i,
j)と定義する（なお、主応力和（σ1 ＋σ2 ＋σ3 ）は
（σx ＋σy ＋σz ）に等しい。）。このF(i,j)は、上
記したように、有限要素法等の数値応力解析により求ま
る。The principal stress sum (σ 1 + σ 2 + σ 3 ) at element j when only external force P (i) = 1 is applied to free contact point i is represented by F (i,
j) (Note that the sum of the principal stresses (σ 1 + σ 2 + σ 3 ) is equal to (σ x + σ y + σ z ).) This F (i, j) is obtained by numerical stress analysis such as the finite element method as described above.
【００１４】さて、F(i,j)が求まると、次式（１）を満
たすP(i)を求める。 P(1)F(1,1)+ …+P(i) F(i,1)+ …+P(m)F(m,1)=Z(1) ・ ・ ・ ・ ・ ・ ・ ・ P(1)F(1,j)+ …+P(i) F(i,j)+ …+P(m)F(m,j)=Z(j) ・ ・ ・ ・ ・ ・ ・ ・ P(1)F(1,n)+ …+P(i) F(i,n)+ …+P(m)F(m,n)=Z(n) ・・・・（１） すなわち、重ね合わせの原理により、実際に熱弾性効果
を利用して求めたZ(j)に等しくなるような外力P(i)の分
布を求めようとする。When F (i, j) is obtained, P (i) satisfying the following equation (1) is obtained. P (1) F (1,1) +… + P (i) F (i, 1) +… + P (m) F (m, 1) = Z (1) ・ ・ ・ ・ ・ ・ ・ ・ P (1) F (1, j) +… + P (i) F (i, j) +… + P (m) F (m, j) = Z (j) ・ ・ ・ ・ ・ ・ ・ ・ P ( 1) F (1, n) +… + P (i) F (i, n) +… + P (m) F (m, n) = Z (n) (1) That is, superposition According to the principle of, an attempt is made to obtain a distribution of the external force P (i) that is equal to Z (j) actually obtained by using the thermoelastic effect.
【００１５】しかしながら、実際には、測定誤差や計算
誤差が生じ得るので、式（１）を厳密に満たすP(i)を求
めることは意味が薄い。そこで、誤差を考慮して、式
（１）を次の式（２）のように改める。However, in practice, a measurement error or a calculation error may occur, and it is meaningless to find P (i) that strictly satisfies the equation (1). Therefore, in consideration of the error, the equation (1) is revised as the following equation (2).
【００１６】 P(1)F(1,1)+ …+P(i) F(i,1)+ …+P(m)F(m,1)-Z(1) =ε(1) ・ ・ ・ ・ ・ ・ ・ ・ ・ ・ P(1)F(1,j)+ …+P(i) F(i,j)+ …+P(m)F(m,j)-Z(j) =ε(j) ・ ・ ・ ・ ・ ・ ・ ・ P(1)F(1,m)+ …+P(i) F(i,m)+ …+P(m)F(m,n)-Z(n) =ε(n) ・・・・（２） そして、最小自乗法を適用して、 を最小にするようにP(i)を見積もる。すなわち、 ∂E/∂P(i)=0 ・・・・（４） を満たすP(i)（ｉ＝１〜ｍ）を求めることにする。P (1) F (1,1) +... + P (i) F (i, 1) +... + P (m) F (m, 1) -Z (1) = ε (1)・ ・ ・ ・ ・ ・ ・ ・ ・ P (1) F (1, j) +… + P (i) F (i, j) +… + P (m) F (m, j) -Z (j) = ε (j) ・ ・ ・ ・ ・ ・ ・ ・ ・ P (1) F (1, m) +… + P (i) F (i, m) +… + P (m) F (m, n)- Z (n) = ε (n) (2) Then, applying the least squares method, P (i) is estimated to minimize. That is, P (i) (i = 1 to m) that satisfies ∂E / ∂P (i) = 0 (4) is determined.
【００１７】式（４）において、ｉ＝１の時、 となる。In equation (4), when i = 1, Becomes
【００１８】以下、ｉ＝ｍまで同様に整理すると、次の
ような連立一次方程式（５）が導出できる。 この式（５）をＬＵ（Ｌｏｗｅｒ−Ｕｐｐｅｒ）分解
法、ガウス法等で解くと、P(i)、すなわち、実際に求め
たZ(j)に等しいか近接した値を与える外力P(i)の分布が
求まる。Hereinafter, by similarly organizing up to i = m, the following simultaneous linear equation (5) can be derived. When this equation (5) is solved by an LU (Lower-Upper) decomposition method, a Gauss method, or the like, an external force P (i) giving a value equal to or close to P (i), that is, Z (j) actually obtained. Is obtained.
【００１９】次いで、この外力分布P(i)をモデル１の境
界条件として、有限要素法等の数値応力解析を行うと、
モデル１の内部及びその表面の任意の点の応力成分
σx ，σy ，σz ，τxy，τyz，τzx、変位εx ，
εy ，εz 等を求めることができる。Next, using this external force distribution P (i) as a boundary condition of the model 1, a numerical stress analysis such as a finite element method
Stress components σ x , σ y , σ z , τ xy , τ yz , τ zx , displacement ε x ,
ε y , ε z, etc. can be obtained.
【００２０】以上の応力分布を求める方法の手順をフロ
ーチャートに示すと図２のようになる。すなわち、ま
ず、ステップ１において、例えば特公昭６２−１２０４
〜５号、同６３−７３３３号等の方法を用いて、熱弾性
効果を利用して実物表面の温度変化ΔＴパターンを検出
し、次に、ステップ２において、ΔＴ＝−ＫＴ（σ1 ＋
σ2 ＋σ3 ）の関係から、実物表面の主応力和（σx ＋
σy ＋σz ＝Z(j)）を求める。さらに、ステップ３にお
いて、この主応力和を求めた実物と同形状のモデルの数
値応力解析に必要な接点の座標、拘束条件、弾性定数
（ヤング率、ポアソン比等）、外力P(i)のかかる座標、
ステップ２で求めた内点ｊでの主応力和Ｚ（ｊ）を入力
する。そして、ステップ４において、例えば有限要素法
を適用して、数値応力解析により特定の１つの外力にＰ
（ｉ）＝１を印加した時の主応力和F(i,j)を求める。こ
の時、弾性体が釣合い条件を保つように境界の任意の部
分を拘束しておく（拘束部分の節点に作用する力は、最
終的に解が求まった時点で正しい値が求まる。）。そし
て、ステップ５において、これらZ(j)）、F(i,j)から、
重ね合わせ原理及び最小自乗法により、式（５）に基づ
き、実測主応力和分布Z(j)に近い主応力和分布を与える
外力P(i)の分布を求める。その後、ステップ６におい
て、ステップ５において得られた外力分布P(i)から数値
応力解析により応力成分σx，σy ，σz ，τxy，
τyz，τzx等を求める。FIG. 2 is a flowchart showing the procedure of the method for obtaining the stress distribution described above. That is, first, in step 1, for example, JP-B-62-1204
No. 5, No. 5, No. 63-7333, etc., the temperature change ΔT pattern of the actual surface is detected by utilizing the thermoelastic effect, and then, in step 2, ΔT = −KT (σ 1 +
From the relationship σ 2 + σ 3 , the sum of the principal stresses on the actual surface (σ x +
σ y + σ z = Z (j)). Further, in step 3, the coordinates of the contact points, constraint conditions, elastic constants (Young's modulus, Poisson's ratio, etc.), and external force P (i) required for numerical stress analysis of the model having the same shape as the real product for which the sum of the principal stresses was obtained. Such coordinates,
The principal stress sum Z (j) at the inner point j obtained in step 2 is input. Then, in step 4, for example, a finite element method is applied, and P
(I) The main stress sum F (i, j) when 1 is applied is obtained. At this time, an arbitrary portion of the boundary is constrained so that the elastic body keeps the balance condition (the correct value is obtained for the force acting on the node of the constrained portion when the solution is finally obtained). Then, in step 5, from these Z (j)) and F (i, j),
The distribution of the external force P (i) that gives the main stress sum distribution close to the measured main stress sum distribution Z (j) is obtained based on the equation (5) by the superposition principle and the least square method. Thereafter, in step 6, the stress components σ x , σ y , σ z , τ xy , and σ x , σ y , σ xy are obtained from the external force distribution P (i) obtained in step 5 by numerical stress analysis.
τ yz , τ zx, etc. are obtained.
【００２１】以上が本発明の弾性体表面の温度変化パタ
ーンから応力分布を求める方法の原理であるが、２次元
実物についての具体例を示す。図３に示すような中心に
円孔を有する矩形板ＡＢＣＤ内の内点５６点について、
主応力和（σx ＋σy ＝Z(j)）を熱弾性効果を利用した
方法により求める。そのデータは次の表−１の通りであ
る。なお、ヤング率は２１０００．０Ｎ／ｍｍ2 、ポア
ソン比は０．３である。The principle of the method for obtaining a stress distribution from a temperature change pattern on the surface of an elastic body according to the present invention has been described above. A specific example of a two-dimensional actual product will be described below. Regarding 56 points inside the rectangular plate ABCD having a circular hole at the center as shown in FIG.
The principal stress sum (σ x + σ y = Z (j)) is determined by a method utilizing the thermoelastic effect. The data is as shown in Table 1 below. The Young's modulus is 21000.0 N / mm 2 and the Poisson's ratio is 0.3.
【００２２】 この矩形板ＡＢＣＤの数値応力解析を行うために、図４
に示すように、外力P(1)〜P(30) を定める。[0022] In order to perform a numerical stress analysis of this rectangular plate ABCD, FIG.
As shown in (1), external forces P (1) to P (30) are determined.
【００２３】次いで、上記の各P(i)のみにP(i)＝１の外
力をかけた時の内点ｊにおける主応力和（σx ＋σy ）
をF(i,j)と定義し、例えば境界要素法を用いて各F(i,j)
を求める。ここまでに得られているデータは次の表−２
の通りである。Next, the principal stress sum (σ x + σ y ) at the inner point j when an external force of P (i) = 1 is applied only to each of the above P (i)
Is defined as F (i, j), and for example, each F (i, j)
Ask for. The data obtained so far is shown in Table 2 below.
It is as follows.
【００２４】 この結果、式（５）は次の式（６）のように書ける。[0024] As a result, equation (5) can be written as the following equation (6).
【００２５】 式（６）のマトリックスをガウス法により解くと、P
(1)，P(2)…P(30) が得られる。表−１に対する境界の
垂直力成分（ＮＦ）及び接線力成分（ＳＦ）は表−３の
通りである。[0025] Solving the matrix of Equation (6) by the Gaussian method gives P
(1), P (2) ... P (30) are obtained. Table 3 shows the normal force component (NF) and the tangential force component (SF) of the boundary with respect to Table 1.
【００２６】 この求まった外力分布P(i)を矩形板ＡＢＣＤの境界条件
として、有限要素法等の数値応力解析によりこの矩形板
ＡＢＣＤ内部の任意の点の応力成分σx ，σy，τxy、
ひずみεx ，εy 等を求めることができる。[0026] Using the obtained external force distribution P (i) as a boundary condition of the rectangular plate ABCD, stress components σ x , σ y , τ xy , at arbitrary points inside the rectangular plate ABCD are obtained by numerical stress analysis such as a finite element method.
The strains ε x and ε y can be obtained.
【００２７】以上、本発明の弾性体表面の温度変化パタ
ーンから応力分布を求める方法の原理と実施例について
説明したが、本発明はこれら実施例に限定されず種々の
変形が可能である。なお、弾性体実物に応力変化を与え
て熱弾性効果による実物表面の温度変化パターンを検出
し、それから実物表面の主応力和分布を求める方法とし
ては、本出願人の提案に係る赤外線カメラを利用する方
法以外にも、その他の公知の方法を利用することができ
る。また、構造体モデルに境界条件を与えることによ
り、その内部及び表面における応力分布を数値解析的に
求める方法も、有限要素法、境界要素法又は差分法に限
定されず、その他の種々の方法を利用することができ
る。Although the principle and embodiments of the method for obtaining the stress distribution from the temperature change pattern on the surface of the elastic body according to the present invention have been described above, the present invention is not limited to these embodiments, and various modifications are possible. In addition, as a method of applying a stress change to the elastic real object to detect a temperature change pattern of the real surface due to the thermoelastic effect, and then obtaining a main stress sum distribution of the actual surface, the infrared camera according to the proposal of the present applicant is used. In addition to the method described above, other known methods can be used. Also, the method of obtaining the stress distribution inside and on the surface by numerical analysis by giving the boundary condition to the structure model is not limited to the finite element method, the boundary element method or the difference method, but various other methods may be used. Can be used.
【００２８】[0028]
【発明の効果】以上の説明から明らかなように、本発明
の弾性体表面の温度変化パターンから応力分布を求める
方法によると、熱弾性効果による弾性体表面の温度変化
パターンデータから求めた実測主応力和分布に最も近い
主応力和分布を与える境界の各自由接点にかかる外力分
布を求め、得られた外力分布から数値応力解析により実
物の任意の点にかかる応力成分を求めるので、実物表面
及び内部における応力成分の分布を簡単な方法で精度よ
く求めることができる。As is clear from the above description, according to the method of obtaining the stress distribution from the temperature change pattern of the elastic body surface according to the present invention, the actual measurement based on the temperature change pattern data of the elastic body surface due to the thermoelastic effect is obtained. The external force distribution applied to each free contact at the boundary that gives the principal stress sum distribution closest to the stress sum distribution is obtained, and the stress component applied to any point of the actual object is obtained from the obtained external force distribution by numerical stress analysis. The distribution of the stress component inside can be accurately obtained by a simple method.
【図１】本発明において用いるパラメータを説明するた
めの模式図である。FIG. 1 is a schematic diagram for explaining parameters used in the present invention.
【図２】本発明のより応力分布を求める方法の手順を示
すフローチャートである。FIG. 2 is a flowchart showing a procedure of a method for obtaining a stress distribution according to the present invention.
【図３】１つの実施例の矩形板の形状と内点を示す図で
ある。FIG. 3 is a diagram showing the shape and inner points of a rectangular plate according to one embodiment.
【図４】図３の矩形板にかかる外力を定める図である。FIG. 4 is a diagram for determining an external force applied to the rectangular plate of FIG. 3;
１…モデル（実物） 1 ... Model (real)
Claims (1)
熱弾性効果による実物表面の温度変化パターンを検出
し、その温度変化パターンから実物表面の内点における
主応力和を求め、また、その実物と同形状の構造体モデ
ルの境界に複数の自由接点を定め、特定の１つの自由接
点に単位外力を印加した時の実物表面の内点における主
応力和を数値応力解析により求め、次いで、重ね合わせ
原理と最小自乗法により、実測主応力和分布に最も近い
主応力和分布を与える各自由接点にかかる外力分布を求
め、得られた外力分布から数値応力解析により実物の任
意の点にかかる応力成分を求めることを特徴とする弾性
体表面の温度変化パターンから応力分布を求める方法。1. An adiabatic stress change is applied to a real elastic body to detect a temperature change pattern on a real surface due to a thermoelastic effect, and a principal stress sum at an inner point of the real surface is obtained from the temperature change pattern. A plurality of free contacts are defined at the boundary of the structure model having the same shape as the real object, and a principal stress sum at an inner point of the real surface when a unit external force is applied to one specific free contact is obtained by numerical stress analysis, and then By using the superposition principle and the least squares method, the external force distribution applied to each free contact that gives the principal stress sum distribution closest to the measured main stress sum distribution is obtained, and the obtained external force distribution is used to calculate the actual stress to an arbitrary point on the real object by numerical stress analysis. A method for obtaining a stress distribution from a temperature change pattern on the surface of an elastic body, wherein the stress distribution is obtained.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP5239392A JP2698029B2 (en) | 1993-09-27 | 1993-09-27 | A method for obtaining stress distribution from temperature change patterns on the surface of an elastic body |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| JP5239392A JP2698029B2 (en) | 1993-09-27 | 1993-09-27 | A method for obtaining stress distribution from temperature change patterns on the surface of an elastic body |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| JPH0792039A JPH0792039A (en) | 1995-04-07 |
| JP2698029B2 true JP2698029B2 (en) | 1998-01-19 |
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ID=17044105
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|---|---|---|---|
| JP5239392A Expired - Fee Related JP2698029B2 (en) | 1993-09-27 | 1993-09-27 | A method for obtaining stress distribution from temperature change patterns on the surface of an elastic body |
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| JP (1) | JP2698029B2 (en) |
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|---|---|---|---|---|
| KR100340217B1 (en) * | 2000-05-29 | 2002-06-12 | 윤숙희 | Numerical Analysis Method For Analyzing Residual Stress of Welding |
| JP4898320B2 (en) * | 2006-06-28 | 2012-03-14 | Ｊｆｅスチール株式会社 | Structure defect detection method and apparatus, and cargo handling machine having defect detection function |
| KR100821958B1 (en) * | 2007-05-15 | 2008-04-15 | 학교법인조선대학교 | Finite element method |
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| JPH05223661A (en) * | 1992-02-17 | 1993-08-31 | Babcock Hitachi Kk | Method for measuring residual stress |
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