鈍形和銳形切口尖端應(yīng)力場邊界元法分析
發(fā)布時間：2019-03-21 11:19
【摘要】：工程結(jié)構(gòu)中經(jīng)常會遇到含切口構(gòu)件,切口端部嚴(yán)重的應(yīng)力集中或應(yīng)力奇異會影響構(gòu)件的安全,對切口根部的應(yīng)力場展開研究具有重要的理論意義和很強的工程應(yīng)用價值。本文利用邊界元法計算鈍形切口端部的熱彈應(yīng)力集中系數(shù)和銳形切口的熱彈奇異應(yīng)力場以及應(yīng)力強度因子,分析切口端部應(yīng)力集中以及奇異應(yīng)力場與切口深度、切口角度的關(guān)系。本文主要研究內(nèi)容如下:首先梳理了彈性力學(xué)邊界元法基本理論和實施過程,利用邊界元法計算平面鈍形切口端部的彈性應(yīng)力場。選取切口開口角度為30°、60°、90°、135°,切口端部圓孔半徑為0.05mm、0.5mm、1.0mm、2.5mm的鈍形切口模型,計算鈍形切口角平分線上內(nèi)點的應(yīng)力值。研究發(fā)現(xiàn)最大周向應(yīng)力出現(xiàn)在切口根部圓弧邊界上,周向應(yīng)力隨著距切口端部距離的增加而減小,并最終趨于角平分線上的平均應(yīng)力,而角平分線上的徑向應(yīng)力值由零增加到極值后再逐漸減小。另外,當(dāng)切口開角為銳角時,周向應(yīng)力、徑向應(yīng)力隨切口張角的增大有微弱減小,但切向應(yīng)力隨切口張角的增大而明顯減小。當(dāng)切口開角為鈍角時,不同圓孔半徑內(nèi)點的周向應(yīng)力值與該切口周向應(yīng)力極值的比值不隨圓孔半徑的變化而變化。其次引入自然熱應(yīng)力邊界積分方程,分析了單、雙材料平面鈍形切口端部的熱應(yīng)力場,發(fā)現(xiàn)鈍形切口端部的熱應(yīng)力變化規(guī)律與彈性應(yīng)力場相似。又計算了平面銳形切口的奇性次數(shù)和熱應(yīng)力強度因子,發(fā)現(xiàn)對稱銳形切口只有I型熱應(yīng)力強度因子K1,且其值隨著開口角度的增加而減小,而銳形斜切口同時有I型和II型應(yīng)力強度因子,且熱應(yīng)力強度因子K1隨著斜切口傾角的增加而減少,而熱應(yīng)力強度因子K2卻隨切口傾角的增加而增加。文章同時利有限元法對結(jié)構(gòu)模型進行了計算,通過和有限元結(jié)果對比,驗證了邊界元結(jié)果的準(zhǔn)確性。邊界元法只需沿區(qū)域的邊界劃分單元,可用較少的單元獲得較高的計算精度,大大減輕了工程結(jié)構(gòu)分析的計算量。
[Abstract]:The severe stress concentration or stress singularity at the end of the notch will affect the safety of the component. It has important theoretical significance and strong engineering application value for the study of the stress field at the root of the notch. The research on the stress field at the root of the notch has important theoretical significance and strong engineering application value. In this paper, the thermal elastic stress concentration coefficient at the end of the blunt notch, the thermal elastic singular stress field and the stress intensity factor of the sharp notch are calculated by the boundary element method, and the stress concentration at the end of the notch, the singular stress field and the depth of the notch are analyzed. The relationship between the angle of the incision. The main contents of this paper are as follows: firstly, the basic theory and implementation process of boundary element method (BEM) for elastic mechanics are combed, and the elastic stress field at the end of a plane blunt notch is calculated by using BEM. The open angle of the incision is 30 擄, 60 擄, 90 擄, 135 擄, and the radius of the round hole at the end of the incision is 0.05mm, 0.5mm, 1.0mm, 2.5mm. The stress value of the internal point on the bisection line of the obtuse notch angle is calculated. It is found that the maximum circumferential stress appears on the arc boundary at the root of the notch, and the circumferential stress decreases with the increase of the distance from the end of the notch, and finally tends to the average stress on the equalizing line of the angle. On the other hand, the radial stress value increases from zero to extreme value and then decreases gradually. In addition, when the opening angle of the notch is sharp, the circumferential stress and radial stress decrease slightly with the increase of the notch tension angle, but the tangential stress decreases obviously with the increase of the notch tension angle. When the opening angle of the notch is obtuse angle, the ratio of the circumferential stress value to the circumferential stress extremum of different circular hole radius does not change with the change of the circular hole radius. Secondly, the natural thermal stress boundary integral equation is introduced to analyze the thermal stress field at the end of blunt notch of single and double materials. It is found that the variation of thermal stress at the end of blunt notch is similar to that of elastic stress field. The singularity number and thermal stress intensity factor of plane sharp notch are calculated. It is found that there is only I type thermal stress intensity factor K _ 1 in symmetrical sharp notch, and its value decreases with the increase of opening angle. There are both I and II stress intensity factors in sharp oblique notch, and the thermal stress intensity factor K _ 1 decreases with the increase of inclined notch angle, while the thermal stress intensity factor K _ 2 increases with the increase of notch inclination angle. At the same time, the finite element method is used to calculate the structural model. By comparing with the finite element results, the accuracy of the boundary element results is verified. The boundary element method (BEM) only needs to divide the elements along the boundary of the region, and can obtain a higher calculation precision with less elements, which greatly reduces the computational complexity of the engineering structure analysis.
【學(xué)位授予單位】：合肥工業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TU31
本文編號：2444886
[Abstract]:The severe stress concentration or stress singularity at the end of the notch will affect the safety of the component. It has important theoretical significance and strong engineering application value for the study of the stress field at the root of the notch. The research on the stress field at the root of the notch has important theoretical significance and strong engineering application value. In this paper, the thermal elastic stress concentration coefficient at the end of the blunt notch, the thermal elastic singular stress field and the stress intensity factor of the sharp notch are calculated by the boundary element method, and the stress concentration at the end of the notch, the singular stress field and the depth of the notch are analyzed. The relationship between the angle of the incision. The main contents of this paper are as follows: firstly, the basic theory and implementation process of boundary element method (BEM) for elastic mechanics are combed, and the elastic stress field at the end of a plane blunt notch is calculated by using BEM. The open angle of the incision is 30 擄, 60 擄, 90 擄, 135 擄, and the radius of the round hole at the end of the incision is 0.05mm, 0.5mm, 1.0mm, 2.5mm. The stress value of the internal point on the bisection line of the obtuse notch angle is calculated. It is found that the maximum circumferential stress appears on the arc boundary at the root of the notch, and the circumferential stress decreases with the increase of the distance from the end of the notch, and finally tends to the average stress on the equalizing line of the angle. On the other hand, the radial stress value increases from zero to extreme value and then decreases gradually. In addition, when the opening angle of the notch is sharp, the circumferential stress and radial stress decrease slightly with the increase of the notch tension angle, but the tangential stress decreases obviously with the increase of the notch tension angle. When the opening angle of the notch is obtuse angle, the ratio of the circumferential stress value to the circumferential stress extremum of different circular hole radius does not change with the change of the circular hole radius. Secondly, the natural thermal stress boundary integral equation is introduced to analyze the thermal stress field at the end of blunt notch of single and double materials. It is found that the variation of thermal stress at the end of blunt notch is similar to that of elastic stress field. The singularity number and thermal stress intensity factor of plane sharp notch are calculated. It is found that there is only I type thermal stress intensity factor K _ 1 in symmetrical sharp notch, and its value decreases with the increase of opening angle. There are both I and II stress intensity factors in sharp oblique notch, and the thermal stress intensity factor K _ 1 decreases with the increase of inclined notch angle, while the thermal stress intensity factor K _ 2 increases with the increase of notch inclination angle. At the same time, the finite element method is used to calculate the structural model. By comparing with the finite element results, the accuracy of the boundary element results is verified. The boundary element method (BEM) only needs to divide the elements along the boundary of the region, and can obtain a higher calculation precision with less elements, which greatly reduces the computational complexity of the engineering structure analysis.
【學(xué)位授予單位】：合肥工業(yè)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：TU31
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