On Member-Fracture and Contact Algorithms for ASI-Gauss Finite Element Method


 先の世界貿易センタービル崩壊を受け,飛行物体との衝突過程をシミュレートすることを目的とし,衝突荷重下の骨組構造体に対して有効な有限要素解析手法が開発された.本手法には,計算コストを低く抑えることが可能なASI法(順応型Shifted Integration法)をさらに改良した,ASI-Gauss法を適用した.ASI-Gauss法では,2つの要素をサブセット要素として考え,そのガウス積分点に相当する位置に応力評価点を配するように数値積分点をシフトすることで,弾性変位解の精度を向上させている.また,積分点のシフトと同時に断面力を解放することで破断を表現し,幾何学的な位置関係に基づいて要素間をギャップ要素で拘束することで接触を表現可能とした.この方法は,衝突荷重を節点力として加える方法に比べ,衝突物体のパラメータの差異を考慮でき,崩壊過程の解明に有効であると考えられる.本稿では,これらの破断および接触アルゴリズムに焦点を当て,簡単な2部材モデルに対する衝突解析を通じ,要素間の拘束時間を設定するためのパラメータなどについて検討した結果について報告する.

Recently, a new finite element code that can be efficiently applied to structural collapse analyses of framed structures under impact loads has been developed. The code is developed by using the ASI-Gauss technique, a modified version of the formerly developed Adaptively Shifted Integration (ASI) technique for the linear Timoshenko beam element, which computes highly accurate elasto-plastic solutions even with the minimum number of elements per member. The ASI-Gauss technique gains still higher accuracy especially in elastic range, by placing the numerical integration points of the two consecutive elements forming an elastically deformed member in such a way that stresses and strains are evaluated at the Gaussian integration points of the two-element member. Moreover, the technique can be used to express member fracture, by shifting the numerical integration point and by releasing the resultant forces in the element simultaneously. An elemental contact algorithm, which uses geometric relation for determining contact and gap elements for simulating impact phenomena, is also implemented to the code. Practical results can be obtained in impact collapse analyses, however, further estimations should be made to the member-fracture and contact algorithms to improve the accuracy as well as reality in collapse stage. In this paper, some efforts are taken to improve the validity of the algorithms, and it is verified by carrying out simple numerical tests.

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