有限要素法を用いた地震時における家具の挙動解析
Motion Analysis of Furniture under Seismic Excitation using FEM

Abstract


 1995年に発生した阪神淡路大震災では,建物に特別な被害が出なかったにも拘らず,家具の転倒や散乱によって避難が遅くなり,室内で怪我を負った人が多数出た.室内における怪我の原因は,その約半分が家具等の転倒によるものであり,今後,長周期地震動が発生した場合には,特に高層建物内で人身への直接的な被害が多くなることが予想される.このような室内被害を減らすためには,家具の地震時挙動を把握する必要がある.そこで,防災科学技術研究所のE-ディフェンスでは,超高層建物の頂部を部分的に切り出した実大寸法の試験体を3次元震動台上で加振し,家具および外壁,天井,ガラスのような非構造材の挙動や損傷など室内外で起こりうる現象を検証している.しかし,振動台実験で定量的なデータを取得するためには,実験を繰り返し実施する必要があり,莫大なコストや時間を必要とする.そのため経済的な観点から限界があるのが現状である.このようなデメリットを補い,規模や回数の影響を受けずに家具などの非構造材の挙動を確認するために,コンピュータを利用した高精度な数値解析システムの開発が必要とされている.
 一般的に家具などの転倒解析には個別要素法(DEM)が適用され多くの研究がおこなわれているが,DEMでは家具を剛体として扱うために,壁,ガラスや人身と接触する際の変形や応力変化などについて検証することは困難である.本研究では,E-ディフェンスが進めている数値震動台(E-Simulator)開発の一環として,家具の地震時挙動を再現するための有限要素解析コードを開発することを目的とした.解析コードには,大規模な骨組構造解析において計算コストを最小限に抑えることが可能なASI-Gauss法を用い,接触・滑り状態をより詳細に表現するために,ペナルティ接触理論に基づく摩擦力を考慮したアルゴリズムを導入した.その際,ペナルティ定数や動摩擦係数などの物理的パラメータを設定する指針を立て,一律の値を用いて解析に導入し,複数の家具の振動台実験結果と比較することにより設定指針と解析コードの有効性を検証した.さらに,家具に発生する断面力を出力し,有限要素法を用いた家具の地震応答解析コードの特長を確認した.なお,本稿では,解析手法の妥当性を検証するために,家具が複雑な挙動を起こす可能性が高い,比較的短周期の地震動を入力波として選択した.


 Improperly secured furniture, especially on the upper floors of high-rise buildings under long-period ground motion, can become dangerous objects for human life. Many tumbled furniture such as chairs and desks in schools could become fatal obstacles that obstruct children from evacuating. Therefore, it is important to know the overturning behaviors of furniture under seismic excitations, as well as the behaviors and damages of the building itself. From this background, various shake-table tests for such specimen had been carried out, although such tests can be too costly to conduct repeatedly. To restrain the costs, numerical simulation techniques such as discontinuous element method (DEM) had been applied to investigate the motion behaviors of furniture. Its calculation cost is very small; however, there are physically uncertain properties that have to be fixed in the models and it is difficult to obtain the deformations and stress distributions of the models. The finite element method (FEM), on the other hand, is an effective means to evaluate the deformations and stress distributions of the models and requires less number of parameters than the DEM.
 In this research, some excitation tests of furniture on a shake-table were carried out, where furniture such as steel cabinets, a desk and a chair with casters, were excited by various seismic waves in different levels, and in single or multiple directions. The displacement data were recorded by a motion capture system to validate with the numerical results. Furthermore, an effective numerical code to analyze the motion behaviors of furniture subjected to seismic excitations was developed. The numerical code was developed based upon the adaptively shifted integration (ASI) – Gauss technique, which is a finite element scheme that provides higher computational efficiency than the conventional code utilizing beam elements. The frictional contact between objects was fully considered by employing a sophisticated penalty method. One of the features of the developed code is that it is easier, compared to the DEM, to select the contact parameters. Penalty coefficients and dynamic friction coefficients are fixed based upon a simple rule. The penalty coefficients are fixed as the weight of furniture and the dynamic friction coefficients as 80% values of each static friction coefficient, which were measured before the experiments on the shake-table. The coefficients related to damping are fixed as 120% values of the penalty coefficients. These rules were applied throughout all the analyses.
 From the validation between experimental and numerical results, it is shown that although a slight difference in the time duration of motions can be seen in some cases, the rocking of the cabinets and the sliding motion of the furniture with casters as a whole are well simulated. The displacements measured at the top of the separated cabinet using the motion capture system, for example, matched almost perfectly with the numerical results. The developed code practically simulated the behaviors of furniture in different input conditions with contact parameters fixed by a simple rule.