報告書番号

305

タイトル（和文）

常微分方程式数値解に基づく薄肉構造材の応力解析法

タイトル（英文）

NUMERICAL METHODS FOR ORDINARY DIFFERENTIAL EQUATIONS OF THIN-WALLED STRUCTURAL MEMBERS

概要 （図表や脚注は「報告書全文」に掲載しております）

パイプライン，各種埋設管，水圧鉄管など薄肉構造物の中には，長大なはりそのものが一つの機能を持った構造物であるものが少なくない。これらは，単純なはり理論式によるだけでなく，断面変形，そり，せん断変形などを考慮した理論式を用いてより精密な検討がしばしば行なわれる。しかし，そのような理論式は多くの場合，高階多元の常微分方程式であり，必ずしも希望する境界条件で解析的に解けるわけではない。本報告では，薄肉構造材のより高度な理論式を，解析解と同等の精度を有し，かつ，種々の荷重条件，境界条件下で解き得る方法を検討している。正規形に変換された薄肉構造材の常微分方程式の特性を，係数マトリクスの固有値分布に見出し，その特性を生かした２種類の解法を提案し，種々の適用結果を示してその有効性を確認した。

概要 （英文）

A CIVIL ENGINEERING STRUCTURE SUCH AS A BOX GIRDER,A PIPELINE, VARIOUS TYPES OF INTAKE PIPE, A PENSTOCK, AN OIL TANK OR THE LIKE, OFTEN IS MADE OF THE LONG AND LARGE BEAM WHICH IN TURN HAS ONE FUNCTION IN AND OF ITSELF. THESE STRUCTURES ARE GENERALLY MADE OF THIN STEEL PLATE DUE TO THE VARIOUS ADVANTAGES THEY OFFER IN STRUCTURAL MECHANICS. WHEN ANY STRUCTURE OF THIS TYPE IS DESIGNED, HOWEVER, A DETAILED STUDY IS MADE OF THOSE PROBLEMS, SUCH AS LOCAL BUCKLING,ETC., WHICH ARE CHARACTERISTICS OF A THIN STEEL PLATE STRUCTURE. WHEN IT IS ANALYSED AS A BEAM, MOREOVER, THE CIVIL ENGINEERING STRUCTURE IS OFTEN PRECISELY STUDIED BY THE USE OF NOT ONLY SIMPLE THEORETICAL FORMULAS BUT ALSO THOSE WHICH TAKE INTO CONSIDERATION A CROSS-SECTIONAL DEFORMATION,WARPING AND SHEAR DEFORMATION. SUCH THEORETICAL FORMULAS, HOWEVER, AREOFTEN HIGHER ORDER SIMULTANEOUS ORDINARY DIFFERENTIAL EQUATIONS, WHICHCANNOT BE ALWAYS ANALYTICALLY SOLVED UNDER DESIRED BOUNDARY AND/OR LOADING CONDITION. IF SUCH AN APPROXIMATE SOLUTION AS THE FINITE DIFFERENCE METHOD, THE FINITE ELEMENT METHOD,ETC. IS USED TO SOLVE THE EQUATIONS, THE LIMITATION OF BOUNDARY AND LOADING CONDITIONS MAY BE ELIMINATED. HOWEVER, THE SOLUTION REQUIRES A LARGE SIZE MATRIX COMPUTATION AND STILL INVOLVES PROBLEMS, SUCH AS A POOR CAPABILITY OF FOLLOWING THE LOCAL STRESS CONCENTRATION CHARACTERISTIC OF A THIN-WALLED STRUCTURE. THEREFORE, IT IS EXPECTED TO FIND OUT THE METHOD WHICH WILL BE ABLE TO COPE WITH VARIOUS LOADING AND BOUNDARY CONDITIONS WITH THE ACCURACY EQUIVALENT TO THAT OF THE EXACT SOLUTION TO A MORE HIGHLY ADVANCED THEORETICAL FORMULA.THIS PAPER SUMMARIZES THE METHOD WHICH IS AN ANSWER TO THE ABOVE MENTIONED PROBLEMS. THIS METHOD BASICALLY SEEKS AN ANALYTICAL SOLUTIONAND AVOID THE COMPLICATIONS OF INDUCING THE ANALYTICAL SOLUTION BY MAKINGEFFECTIVE USE OF NUMERICAL METHODS. THE METHODS CAN BE APPLIED TO VARIOUS BOUNDARY AND LOADING CONDITIONS.

報告者

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