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論文

Verification of probabilistic fracture mechanics analysis code PASCAL for reactor pressure vessel

Lu, K.; 高見澤 悠; Li, Y.; 眞崎 浩一*; 高越 大輝*; 永井 政貴*; 南日 卓*; 村上 健太*; 関東 康祐*; 八代醍 健志*; et al.

Mechanical Engineering Journal (Internet), 10(4), p.22-00484_1 - 22-00484_13, 2023/08

A probabilistic fracture mechanics (PFM) analysis code, PASCAL, has been developed by Japan Atomic Energy Agency for failure probability and failure frequency evaluation of reactor pressure vessels (RPVs) considering neutron irradiation embrittlement and thermal transients. To strengthen the applicability of PASCAL, considerable efforts on verifications of the PASCAL code have been made in the past years. As a part of the verification activities, a working group consisted of different organizations from industry, universities and institutes, was established in Japan. In the early phase, the working group focused on verifying the PFM analysis functions for RPVs in pressurized water reactors (PWRs) subjected to pressurized thermal shock (PTS) events. Recently, the PASCAL code has been improved in order to run PFM analyses for both RPVs in PWRs and boiling water reactors (BWRs) subjected to a broad range of transients. Simultaneously, the working group initiated a verification plan for the improved PASCAL through independent PFM analyses by different organizations. Concretely, verification analyses for a PWR-type RPV subjected to PTS transients and a BWR-type RPV subjected to a low-temperature over pressure transient were performed using PASCAL. This paper summarizes those verification activities, including the verification plan, analysis conditions and results. Based on the verification studies, the reliability of PASCAL for probabilistic integrity assessments of Japanese RPVs was confirmed with confidence.

論文

Recent improvements of probabilistic fracture mechanics analysis code PASCAL for reactor pressure vessels

Lu, K.; 高見澤 悠; 勝山 仁哉; Li, Y.

International Journal of Pressure Vessels and Piping, 199, p.104706_1 - 104706_13, 2022/10

 被引用回数:3 パーセンタイル:60.63(Engineering, Multidisciplinary)

A probabilistic fracture mechanics (PFM) analysis code PASCAL was developed in Japan for probabilistic integrity assessment of reactor pressure vessels (RPVs) in pressurized water reactors (PWRs) considering neutron irradiation embrittlement and pressurized thermal shock (PTS) transients. To strengthen the practical applications of PFM methodology in Japan, PASCAL has been upgraded to a new version, PASCAL5, which enables PFM analyses of RPVs in both PWRs and boiling water reactors (BWRs) subjected to a broad range of transients, including PTS and normal operational transients. In this paper, the recent improvements in PASCAL5 are described such as the incorporated stress intensity factor solutions and corresponding calculation methods for external surface cracks and embedded cracks near the RPV outer surface. In addition, the analysis conditions and evaluation models recommended for PFM analyses of Japanese RPVs in BWRs are investigated. Finally, PFM analysis examples for core region of a Japanese BWR-type model RPV subjected to two transients (i.e., low-temperature over pressure and heat-up transients) are presented using PASCAL5.

論文

Application of probabilistic fracture mechanics to reactor pressure vessel using PASCAL4 code

Lu, K.; 勝山 仁哉; Li, Y.; 吉村 忍*

Journal of Pressure Vessel Technology, 143(2), p.021505_1 - 021505_8, 2021/04

 被引用回数:1 パーセンタイル:10.51(Engineering, Mechanical)

Probabilistic fracture mechanics (PFM) is considered to be a promising methodology in structural integrity assessments of pressure-boundary components in nuclear power plants since it can rationally represent the inherent probabilistic distributions for influence parameters without over-conservativeness. To strengthen the applicability of PFM methodology in Japan, Japan Atomic Energy Agency has developed a PFM analysis code PASCAL4 which enables the failure frequency evaluation of reactor pressure vessels (RPVs) considering neutron irradiation embrittlement and thermal transients. PASCAL4 is expected to make a significant contribution to the probabilistic integrity assessment of Japanese RPVs. In this study, PFM analysis for a Japanese model RPV in a pressurized water reactor (PWR) was conducted using PASCAL4, and the effects of nondestructive examination (NDE) and neutron flux reduction on failure frequencies of the RPV were quantitatively evaluated. From the analysis results, it is concluded that PASCAL4 is useful for probabilistic integrity assessments of embrittled RPVs and can enhance the applicability of PFM methodology.

論文

Extension of PASCAL4 code for probabilistic fracture mechanics analysis of reactor pressure vessel in boiling water reactor

Lu, K.; 勝山 仁哉; Li, Y.

Proceedings of ASME 2020 Pressure Vessels and Piping Conference (PVP 2020) (Internet), 10 Pages, 2020/08

In Japan, Japan Atomic Energy Agency has developed a probabilistic fracture mechanics (PFM) analysis code, PASCAL4, for probabilistic evaluation of reactor pressure vessels (RPVs) in pressurized water reactors (PWRs) considering neutron irradiation embrittlement and pressurized thermal shock (PTS) events. Besides severe PTS events, however, transients associated with normal operations, such as the cooldown and heatup transients associated with reactor shutdown and startup, respectively, should also be considered in the integrity assessment of RPVs in both PWRs and boiling water reactors (BWRs). With regard to a heatup transient, because temperature is at its minimum, and tensile stress at its maximum on the RPV outer surface, outer surface crack and embedded crack near the RPV outer surface should be taken into account. To extend the applicability of PASCAL4, we improved the code to include analysis functions for these cracks. The improved PASCAL4 can be used to run PFM analyses of RPVs subjected to both cooldown (including PTS) and heatup transients. In this paper, improvements made to PASCAL4 are firstly described, including the incorporated stress intensity factor solutions and the corresponding calculation methods for vessel outer surface crack and embedded crack near the outer surface. Using the improved PASCAL4, PFM analysis examples for a Japanese BWR-type model RPV subjected to thermal transients including a low temperature overpressure event and a heatup transient are presented.

論文

Recent verification activities on probabilistic fracture mechanics analysis code PASCAL4 for reactor pressure vessel

Lu, K.; 勝山 仁哉; Li, Y.; 宮本 裕平*; 廣田 貴俊*; 板橋 遊*; 永井 政貴*; 鈴木 雅秀*; 関東 康祐*

Mechanical Engineering Journal (Internet), 7(3), p.19-00573_1 - 19-00573_14, 2020/06

Probabilistic fracture mechanics (PFM) is considered a promising methodology in assessing the integrity of structural components in nuclear power plants because it can rationally represent the influence parameters in their probabilistic distributions without over-conservativeness. In Japan, Japan Atomic Energy Agency has developed a PFM analysis code PASCAL4 (PFM Analysis of Structural Components in Aging LWRs Version 4) which enables the probabilistic integrity assessment of reactor pressure vessels (RPVs) considering neutron irradiation embrittlement and pressurized thermal shock events. Several efforts have been made to verify PASCAL4 to ensure that this code can provide reliable analysis results. In particular, a Japanese working group, which consists of different participants from the industry and from universities and institutes, has been established to conduct the verification studies. This paper summarizes verification activities of the working group in the past two years. Based on those verification activities, the reliability and applicability of PASCAL4 for structural integrity assessments of Japanese RPVs have been confirmed with great confidence.

論文

Improvements on evaluation functions of a probabilistic fracture mechanics analysis code for reactor pressure vessels

Lu, K.; 勝山 仁哉; Li, Y.

Journal of Pressure Vessel Technology, 142(2), p.021208_1 - 021208_11, 2020/04

 被引用回数:6 パーセンタイル:42.63(Engineering, Mechanical)

In Japan, a probabilistic fracture mechanics (PFM) analysis code PASCAL was developed for structural integrity assessment of reactor pressure vessels (RPVs) considering neutron irradiation embrittlement and pressurized thermal shock (PTS) events. By reflecting the latest knowledge and findings, the evaluation functions are continuously improved and have been incorporated into PASCAL4 which is the most recent version of the PASCAL code. In this paper, the improvements made in PASCAL4 are explained in detail, such as the evaluation model of warm prestressing (WPS) effect, evaluation function of confidence levels for PFM analysis results by considering the epistemic and aleatory uncertainties in probabilistic variables, the recent stress intensity factor (KI) solutions, and improved methods for KI calculations when considering complicated stress distributions. Moreover, using PASCAL4, PFM analysis examples considering these improvements are presented.

論文

Guideline on probabilistic fracture mechanics analysis for Japanese reactor pressure vessels

勝山 仁哉; 小坂部 和也*; 宇野 隼平*; Li, Y.; 吉村 忍*

Journal of Pressure Vessel Technology, 142(2), p.021205_1 - 021205_10, 2020/04

 被引用回数:2 パーセンタイル:15.81(Engineering, Mechanical)

確率論的破壊力学(PFM)に基づく構造健全性評価手法は、経年劣化に関連する様々な因子の確率分布を考慮して原子炉圧力容器(RPV)の破損頻度を評価できる合理的な手法である。我々は、中性子照射脆化や加圧熱衝撃事象(PTS)事象を考慮してRPVの破損頻度を評価するPFM解析コードPASCALを開発してきた。また、国内におけるPFMの適用性向上を図るため、破壊力学に関する知識を有する解析者がそれを参照することでPFM解析を行い亀裂貫通頻度を評価できるよう、標準的解析要領を整備した。本要領は、本文、解説及び付属書で構成されており、PFM解析に関する技術的根拠や最新知見が取りまとめられたものになっている。本論では、本要領の概要について述べるとともに、本要領とPTS評価に関する国内データベースに基づき得られた国内モデルRPVに対する破損頻度の評価結果について述べる。

論文

Application of probabilistic fracture mechanics methodology for Japanese reactor pressure vessels using PASCAL4

Lu, K.; 勝山 仁哉; Li, Y.; 吉村 忍*

Proceedings of 2019 ASME Pressure Vessels and Piping Conference (PVP 2019) (Internet), 9 Pages, 2019/07

Probabilistic fracture mechanics (PFM) methodology, which represents the influence parameters in their inherent probabilistic distributions, is deemed to be promising in the structural integrity assessment of pressure-boundary components in nuclear power plants. To strengthen the applicability of PFM methodology in Japan, Japan Atomic Energy Agency has developed a PFM analysis code called PASCAL4 (PFM Analysis of Structural Components in Aging LWRs Version 4) which can be used to evaluate the failure frequency of reactor pressure vessels (RPVs) considering neutron irradiation embrittlement and pressurized thermal shock events. PASCAL4 is expected to make a significant contribution to the probabilistic integrity assessment of Japanese RPVs. In this study, PFM analyses are performed for a Japanese model RPV using PASCAL4, and the effects of non-destructive examination and neutron fluence mitigation on failure frequency of RPV are quantitatively evaluated. From the analysis results, it is concluded that PASCAL4 is useful for the structural integrity assessment of RPVs and can enhance the applicability of PFM methodology.

論文

Effect of coolant water temperature of ECCS on failure probability of RPV

勝山 仁哉; 眞崎 浩一; Lu, K.; 渡辺 正*; Li, Y.

Proceedings of 2019 ASME Pressure Vessels and Piping Conference (PVP 2019) (Internet), 7 Pages, 2019/07

加圧水型原子炉の原子炉圧力容器(RPV)において、非常用炉心冷却系(ECCS)の冷却材の温度が加圧熱衝撃(PTS)事象時のRPVの構造健全性に影響する可能性がある。PTS事象時の熱衝撃の影響を低減することを目的とした緩和措置として、ECCSの冷却水温度を上げることに着目し、国内の代表的な高経年化したPWRプラントを対象に、システム解析コードRELAP5及び確率論的破壊力学(PFM)解析コードPASCAL4を用いた熱水力解析及びPFM解析を実施した。その結果、高圧注入系と低圧注入系(HPI/LPI)の冷却水温度のみを上昇させた場合には破損確率の低減に効果はない。一方、HPI/LPI及び蓄圧系の冷却水温度を上昇させた場合にはRPVの破損確率が大きく低減することを示した。

論文

Verification of a probabilistic fracture mechanics code PASCAL4 for reactor pressure vessels

Lu, K.; 勝山 仁哉; Li, Y.; 宮本 裕平*; 廣田 貴俊*; 板橋 遊*; 永井 政貴*; 鈴木 雅秀*; 関東 康祐*

Proceedings of 27th International Conference on Nuclear Engineering (ICONE-27) (Internet), 9 Pages, 2019/05

Probabilistic fracture mechanics (PFM) is considered as a promising methodology in the integrity assessment of structural components in a nuclear power plant since it can rationally represent the influence parameters in their inherent probabilistic distributions without over-conservativeness. In Japan, a PFM analysis code called PASCAL4 (PFM Analysis of Structural Components in Aging LWRs Version 4) has been developed by Japan Atomic Energy Agency, which can be used for structural integrity assessments of reactor pressure vessels (RPVs) considering neutron irradiation embrittlement and pressurized thermal shock events. Up till now, many efforts have been made on verifying the PASCAL4 code. Among them, a Japanese working group which is consisted of seven participants from industries, universities and institutes was established to conduct the verification studies. Based on verification activities during the past two years, the reliability and applicability of PASCAL4 for structural integrity assessments of Japanese RPVs were confirmed with great confidence. This paper summarizes the verification activities in this working group including the verification plan, analysis conditions and results.

論文

Development of crack evaluation models for probabilistic fracture mechanics analyses of Japanese reactor pressure vessels

Lu, K.; 眞崎 浩一; 勝山 仁哉; Li, Y.

Proceedings of 2018 ASME Pressure Vessels and Piping Conference (PVP 2018), 8 Pages, 2018/07

In Japan, a probabilistic fracture mechanics (PFM) analysis code PASCAL has been developed by Japan Atomic Energy Agency for structural integrity assessment of reactor pressure vessels (RPVs). The most recent release is PASCAL Version 4 (hereafter, PSACAL4) which can be used to evaluate the failure frequency of RPVs considering neutron irradiation embrittlement and pressurized thermal shock events. For the integrity assessment of RPVs, development of crack evaluation models is important. In this study, finite element analyses are performed firstly to verify the stress intensity factor calculations of cracks in PASCAL4. In addition, the applicability of the crack evaluation models in PASCAL4 such as the location of embedded cracks, crack shape and depth of surface cracks, and the increment of crack propagation is investigated. Based on sensitivity analyses of crack evaluation models for Japanese RPVs using PASCAL4, the effects of these evaluation models on failure frequency are clarified. From the analysis results, crack evaluation models recommended to the failure frequency evaluation for a Japanese model RPV are discussed.

論文

Development of probabilistic fracture mechanics analysis code PASCAL Version 4 for reactor pressure vessels

Lu, K.; 眞崎 浩一; 勝山 仁哉; Li, Y.; 宇野 隼平*

Proceedings of 2018 ASME Pressure Vessels and Piping Conference (PVP 2018), 10 Pages, 2018/07

In Japan, Japan Atomic Energy Agency has developed a PFM analysis code PASCAL (PFM Analysis of Structural Components in Aging LWRs) for structural integrity assessment of Japanese reactor pressure vessels (RPVs) considering neutron irradiation embrittlement and pressurized thermal shock transients. By reflecting the latest knowledge and findings, the PASCAL code has been continuously improved. In this paper, the development of PASCAL Version 4 (hereafter, PASCAL4) is described. Several analysis functions incorporated into PASCAL4 for evaluating the failure frequency of RPVs are introduced, for example, the evaluation function of confidence level of failure frequency considering epistemic and aleatory uncertainties in probabilistic variables, the recent stress intensity factor (KI) solutions and KI calculation methods considering complicated stress distributions, and the recent Japanese irradiation embrittlement prediction method. Finally, using PASCAL4, a PFM analysis example for a Japanese model RPV is presented.

論文

Development of stress intensity factors for subsurface flaws in plates subjected to polynomial stress distributions

Lu, K.; 真野 晃宏; 勝山 仁哉; Li, Y.; 岩松 史則*

Journal of Pressure Vessel Technology, 140(3), p.031201_1 - 031201_11, 2018/06

 被引用回数:9 パーセンタイル:45.47(Engineering, Mechanical)

The stress intensity factor (SIF) solutions for subsurface flaws near the free surfaces of components, which are known to be important in engineering applications, have not been provided yet. Thus, in this paper, SIF solutions for subsurface flaws near the free surfaces in flat plates were numerically investigated based on finite element analyses. The flaws with aspect ratios a/l = 0.0, 0.1, 0.2, 0.3, 0.4 and 0.5, the normalized ratios a/d = 0.0, 0.1, 0.2, 0.4, 0.6 and 0.8, and d/t = 0.01 and 0.10 were taken into account, where a is the half flaw depth, l is the flaw length, d is the distance from the center of the subsurface flaw to the nearest free surface and t is the wall thickness. Fourth-order polynomial stress distribution in the thickness direction was considered. In addition, the developed SIF solutions were incorporated into a Japanese probabilistic fracture mechanics (PFM) code, and PFM analyses were performed for a Japanese reactor pressure vessel containing a subsurface flaw near the inner surface. The PFM analysis results indicate that the obtained SIF solutions are effective in engineering applications.

論文

An Application of the probabilistic fracture mechanics code PASCAL-SP to risk informed in-service inspection for piping

真野 晃宏; 山口 義仁; 勝山 仁哉; Li, Y.

Proceedings of Asian Symposium on Risk Assessment and Management 2017 (ASRAM 2017) (USB Flash Drive), 12 Pages, 2017/11

米国等では原子力発電所の配管系を対象として、リスク情報を活用した供用期間中検査(RI-ISI)が広く実施されている。Westinghouse Owners Groupが開発したRI-ISI手法では、配管系をセグメントに区分し、非破壊試験を考慮した配管セグメントの漏えい頻度に基づいて、試験程度を決定する。配管セグメントの漏えい頻度の評価には、試験における亀裂の検出確率を亀裂寸法によらず一定値とみなす等の仮定に基づく統計モデルが用いられている。一方で、確率論的破壊力学(PFM)解析では、現実に即した亀裂検出確率評価モデルにより、詳細に漏えい頻度を評価可能である。原子力機構では、経年事象や非破壊試験等を考慮して配管セグメントの漏えい頻度を評価可能なPFM解析コードPASCAL-SPを開発している。本研究では、PASCAL-SPを用いて、試験チームの熟練度、試験時期及び補修範囲の考え方について異なる条件の下でセグメントの漏えい頻度及び試験程度を評価した。その結果、試験程度を現実に即して柔軟に評価できることから、PASCAL-SPはRI-ISIにおける有効なツールであると結論付けた。

論文

An Estimation method of flaw distributions reflecting inspection results through Bayesian update

Lu, K.; 宮本 裕平*; 真野 晃宏; 勝山 仁哉; Li, Y.

Proceedings of Asian Symposium on Risk Assessment and Management 2017 (ASRAM 2017) (USB Flash Drive), 9 Pages, 2017/11

近年、原子炉圧力容器(RPV)のような安全上重要機器に対する構造健全性評価において、確率論的破壊力学(PFM)に基づく手法が各国で用いられている。PFM解析では、対象となる機器の想定される欠陥を考慮して、その破損確率や破損頻度を評価する。そのため、PFMに基づきRPVの健全性評価を行う場合、欠陥分布(欠陥深さ及び密度分布)を重要な影響因子として合理的に設定する必要がある。最近、べイズ更新に基づき検査結果を欠陥分布に反映する手法が示され、検査で亀裂が見つかった場合に適用できる尤度関数が提案された。一方、RPVに対する検査の結果として欠陥指示がない可能性があるが、その場合のべイズ更新に必要な尤度関数が提案されていない。そこで、本研究では、検査により欠陥指示があった場合となかった場合の両方に適用できる尤度関数を提案した。また、提案した尤度関数を用いて、べイズ更新により検査結果を反映した欠陥分布を更新した例を示した。以上より、本研究で提案した尤度関数が、欠陥指示がない場合にも適用できることを明らかにした。

論文

Benchmark analyses using probabilistic fracture mechanics analysis codes for reactor pressure vessels

荒井 健作*; 勝山 仁哉; Li, Y.

Proceedings of Asian Symposium on Risk Assessment and Management 2017 (ASRAM 2017) (USB Flash Drive), 8 Pages, 2017/11

原子力機構が開発した確率論的破壊力学(PFM)解析コードPASCAL及び米国のPFM解析コードFAVORを用いて、米国3ループ加圧水型原子炉の原子炉圧力容器を対象としたベンチマーク解析を実施した。応力拡大係数の式等の解析条件を一致させた結果、両コードの解析結果は良好に一致した。

論文

Probabilistic fracture mechanics analysis models for Japanese reactor pressure vessels

Lu, K.; 勝山 仁哉; 宇野 隼平; Li, Y.

Proceedings of 2017 ASME Pressure Vessels and Piping Conference (PVP 2017) (CD-ROM), 8 Pages, 2017/07

Probabilistic fracture mechanics (PFM) analysis code PASCAL has been developed by Japan Atomic Energy Agency for structural integrity assessments of reactor pressure vessels (RPVs) by considering the inherent probabilistic distributions of various influence factors. For practical applications, several evaluation models are improved, and have been implemented into the current PASCAL code. In this paper, the improvements of PASCAL are introduced firstly, such as the evaluation method for underclad cracks, treatments of the complicated welding residual stress distribution, and evaluation models for the warm pre-stressing effect. In addition, the effects of these improvements on failure probability or failure frequency of RPVs are investigated by performing PFM analyses for domestic RPVs using PASCAL. From the analysis results, the effects of the improved evaluation models are discussed.

論文

Guideline on probabilistic fracture mechanics analysis for Japanese reactor pressure vessels

勝山 仁哉; 小坂部 和也*; 宇野 隼平; Li, Y.; 吉村 忍*

Proceedings of 2017 ASME Pressure Vessels and Piping Conference (PVP 2017) (CD-ROM), 9 Pages, 2017/07

確率論的破壊力学(PFM)に基づく構造健全性評価手法は、経年劣化に関連する様々な因子の確率分布を考慮して原子炉圧力容器(RPV)の破損頻度を評価できる合理的な手法である。我々は、中性子照射脆化や加圧熱衝撃事象(PTS)を考慮してRPVの破損頻度を評価するPFM解析コードPASCALを開発してきた。また我々は、国内におけるPFMの適用性向上を図るため、破壊力学に関する知識を有する解析者がそれを参照することでPFM解析を行い亀裂貫通頻度を評価できるよう、標準的解析要領を整備した。本要領は、本文、解説及び付属書で構成されており、PFM解析に関する技術的根拠や最新知見が取りまとめられたものになっている。本論では、本要領の概要について述べるとともに、本要領とPTS評価に関する国内データベースに基づき得られた国内モデルRPVに対する破損頻度の評価結果について述べる。

論文

地震動の不確かさを考慮した経年配管の構造信頼性評価手法の開発

杉野 英治*; 伊藤 裕人*; 鬼沢 邦雄; 鈴木 雅秀

日本原子力学会和文論文誌, 4(4), p.233 - 241, 2005/12

本研究の目的は、既存の軽水炉原子力発電プラントの長期利用の観点から、安全上重要な機器構造物の経年変化事象を適切に考慮した地震時構造信頼性評価手法を確立することである。そこで、1次冷却系配管における応力腐食割れや地震荷重による疲労き裂進展などの経年変化事象に着目し、確率論的破壊力学に基づいた配管破損確率評価コードPASCAL-SCと、プラントサイトの地震発生確率及び地震発生確率レベルに応じた地震動を算出するための確率論的地震ハザード評価コードSHEAT-FMを開発し、これらを組合せた経年配管の地震時構造信頼性評価手法を提案した。この手法を用いてBWRモデルプラントの再循環系配管溶接線の1つについて評価した。その結果、経年配管の破損確率は、運転時間がある時期を過ぎると急激に増加する傾向にあり、相対的に地震荷重よりも経年変化による破損の影響が大きいことがわかった。

論文

Development of Stress intensity factor coefficients database for a surface crack of an RPV considering the stress discontinuity between cladding and base metal

鬼沢 邦雄; 柴田 勝之*; 鈴木 雅秀

Proceedings of 2005 ASME/JSME Pressure Vessels and Piping Division Conference (PVP 2005), 12 Pages, 2005/07

原子炉圧力容器に対する加圧熱衝撃事象においては、内面肉盛溶接材と母材との境界で、熱膨張係数の違いにより応力の不連続が生じる。健全性評価のための破壊力学解析においては、この境界付近に存在するき裂に対しては、応力不連続を考慮して応力拡大係数を算出する必要がある。確率論的破壊力学解析においては、膨大な数の破壊力学解析を実施するため、この算出に時間をかけずに、かつ精度の高い手法が必要である。このため、半楕円表面き裂に対する応力不連続に対応できる無次元化応力拡大係数を作成した。この無次元化応力拡大係数は、3次元モデルによるFEM解析から求めた。表面点では、表面付近内部の応力拡大係数から外挿して求める。この無次元化応力拡大係数を用いて、表面及び最深点における応力拡大係数を精度よく、短時間で算出できる。

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