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	<title>GRSA &#8211; TERAZAWA Lab.</title>
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	<description>寺澤研究室</description>
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	<title>GRSA &#8211; TERAZAWA Lab.</title>
	<link>https://www.zawawatech.arch.ens.titech.ac.jp</link>
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	<item>
		<title>DEVELOPMENT OF A MACHINE-LEARNING-BASED WEB APPLICATION TOOL FOR PARAMETRIC DAMPER DESIGN</title>
		<link>https://www.zawawatech.arch.ens.titech.ac.jp/development-of-a-machine-learning-based-web-application-tool-for-parametric-damper-design/</link>
		
		<dc:creator><![CDATA[ZawawatechEditor]]></dc:creator>
		<pubDate>Tue, 13 Aug 2024 09:16:22 +0000</pubDate>
				<category><![CDATA[Research]]></category>
		<category><![CDATA[DS/AI]]></category>
		<category><![CDATA[GRSA]]></category>
		<category><![CDATA[Seismic optimization]]></category>
		<guid isPermaLink="false">https://www.zawawatech.arch.ens.titech.ac.jp/?p=798</guid>

					<description><![CDATA[<p><img src="https://www.zawawatech.arch.ens.titech.ac.jp/wp-content/uploads/2024/08/34_NSAIDD-1024x548.png" class="webfeedsFeaturedVisual" /></p>　日鉄エンジニアリングとの共同で、免・制振部材の膨大な配置ケースの地震応答を人工知能により数分以内に算出し、設計者が基本計画時の設計条件（耐震性能・コスト）を満たすおおよその部材配置を検討するためのWebアプリケーション [&#8230;]]]></description>
										<content:encoded><![CDATA[<p><img src="https://www.zawawatech.arch.ens.titech.ac.jp/wp-content/uploads/2024/08/34_NSAIDD-1024x548.png" class="webfeedsFeaturedVisual" /></p>
<figure class="wp-block-video"><video autoplay controls controlslist="nodownload" oncontextmenu="return false;" muted src="https://www.zawawatech.arch.ens.titech.ac.jp/wp-content/uploads/2024/08/34_NSAIDD.mp4"></video></figure>



<p>　日鉄エンジニアリングとの共同で、免・制振部材の膨大な配置ケースの地震応答を人工知能により数分以内に算出し、設計者が基本計画時の設計条件（耐震性能・コスト）を満たすおおよその部材配置を検討するためのWebアプリケーションNS-AIDD （エヌエス-エイド、AI-based Damper Design System）を開発いたしました。私が発明者と開発者の1人です。 ここ数年にわたって、耐震設計のパラメトリックデザインとも呼べる「対話的な耐震最適化手法」を検討しており、NS-AIDDはこれからの耐震設計ツールの一方向性を示唆するために開発しました。 長いこと悩んで作っていましたが、Done is better than perfectということで、とにかく世に出してみることにしました。結果的にですが、NS-AIDDは、耐震設計の領域において、人工知能を実用レベルで活用した初めての事例であり、これから様々な議論の的として使っていただき、皆様と暖かく育てていければと思います。このページの動画は2024年7月にイタリアで開催された世界地震工学会議での発表スライドです。また，日本語では<a rel="noreferrer noopener" href="https://t2r2.star.titech.ac.jp/rrws/file/CTT100884230/ATD100000413/" target="_blank"><strong>2022年10月号の鉄構技術</strong></a>に特集記事を執筆しましたのでご笑覧いただければ幸いです。最後に開発にあたりご助言いただいたAI研究会の皆様に感謝申し上げます。<strong><a rel="noreferrer noopener" href="https://www.researchgate.net/publication/382068056_DEVELOPMENT_OF_A_MACHINE-LEARNING-BASED_WEB_APPLICATION_TOOL_FOR_PARAMETRIC_DAMPER_DESIGN" data-type="URL" data-id="https://www.researchgate.net/publication/382068056_DEVELOPMENT_OF_A_MACHINE-LEARNING-BASED_WEB_APPLICATION_TOOL_FOR_PARAMETRIC_DAMPER_DESIGN" target="_blank">会議論文はこちら</a></strong></p>



<p>According to the common use of seismic energy-dissipation devices (i.e. dampers), in Japan, practical computational optimal damper design methods satisfying multiple design constraints are attracting attention, and are becoming to be actually used. Nevertheless, while these methods produce an optimal design solution exactly following the optimization problem, another (not optimal) design option is often adopted in design practice because it is still a challenge to include highly indeterminate engineering judgments into the procedure. On the other hand, the manual trial-and-error study with numerical simulation can proceed with the damper design while incorporating the engineering judgments, but perhaps miss better design options in the limited design period. Therefore, the Tokyo Institute of Technology and Nippon Steel Engineering developed a web application tool called NS-AIDD ® (AI-based Damper Design System), where machine-learning models quickly evaluates seismic responses of a huge number of damper design options, and the results are organized on the clear graphical user interface, for the efficient seismic design of supplementary damped structures and seismically isolated structures while combining the digital tools and engineering judgment. This paper presents the motivation in Japanese design practice, an overview of the tool, and the limitations of the machine-learning models. <a rel="noreferrer noopener" href="https://www.researchgate.net/publication/382068056_DEVELOPMENT_OF_A_MACHINE-LEARNING-BASED_WEB_APPLICATION_TOOL_FOR_PARAMETRIC_DAMPER_DESIGN" data-type="URL" data-id="https://www.researchgate.net/publication/382068056_DEVELOPMENT_OF_A_MACHINE-LEARNING-BASED_WEB_APPLICATION_TOOL_FOR_PARAMETRIC_DAMPER_DESIGN" target="_blank"><strong>The paper is here.</strong></a></p>
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		<title>Generalized response spectrum analysis based computational morphogenesis for metal gridshells with buckling-restrained braces subjected to seismic loading 一般化応答スペクトル解析法に基づくグリッドシェル構造の形態創生手法</title>
		<link>https://www.zawawatech.arch.ens.titech.ac.jp/%e4%b8%80%e8%88%ac%e5%8c%96%e5%bf%9c%e7%ad%94%e3%82%b9%e3%83%9a%e3%82%af%e3%83%88%e3%83%ab%e8%a7%a3%e6%9e%90%e6%b3%95%e3%81%ab%e5%9f%ba%e3%81%a5%e3%81%8f%e3%82%b0%e3%83%aa%e3%83%83%e3%83%89%e3%82%b7/</link>
		
		<dc:creator><![CDATA[ZawawatechEditor]]></dc:creator>
		<pubDate>Mon, 24 Oct 2022 02:47:00 +0000</pubDate>
				<category><![CDATA[Research]]></category>
		<category><![CDATA[Form-finding]]></category>
		<category><![CDATA[GRSA]]></category>
		<category><![CDATA[Seismic optimization]]></category>
		<guid isPermaLink="false">https://www.zawawatech.arch.ens.titech.ac.jp/?p=543</guid>

					<description><![CDATA[<p><img src="https://www.zawawatech.arch.ens.titech.ac.jp/wp-content/uploads/2024/08/gif11.gif" class="webfeedsFeaturedVisual" /></p>　一般化応答スペクトル解析法に基づくグリッドシェル構造の形態創生手法 を提案しました。本研究は私が推進している耐震最適化の研究シリーズの1つであり、空間構造の複雑な地震応答特性とダンパーの応答低減効果を直接考慮した屋根の [&#8230;]]]></description>
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<p>　<a rel="noreferrer noopener" href="https://doi.org/10.1016/j.compstruc.2022.106914" data-type="URL" data-id="https://doi.org/10.1016/j.compstruc.2022.106914" target="_blank">一般化応答スペクトル解析法に基づくグリッドシェル構造の形態創生手法 </a>を提案しました。本研究は私が推進している耐震最適化の研究シリーズの1つであり、空間構造の複雑な地震応答特性とダンパーの応答低減効果を直接考慮した屋根の形状探索を可能にしました。本研究はこれまで学術的・実用的に難しいとされてきた課題を解決したもので、既往研究を調べている限りではおそらく世界初です。博論で描いた青写真の１つに辿り着きました。本研究が採択率1割、計算力学の老舗CASに掲載されたことを光栄に思います。私の星付き論文です。オープンアクセスにしました。<strong>本研究は2022年の建築学会大会および第17回コロキウム構造形態の解析と創生にて日本語でも発表し，担当の学生は優秀発表賞に選ばれました</strong>！</p>



<p>I would like to share my paper entitled &#8220;<a rel="noreferrer noopener" href="https://doi.org/10.1016/j.compstruc.2022.106914" data-type="URL" data-id="https://doi.org/10.1016/j.compstruc.2022.106914" target="_blank">Generalized response spectrum analysis based computational morphogenesis for metal gridshells with buckling-restrained braces subjected to seismic loading</a>&#8221; published in Computers &amp; Structures. Structural morphogenesis is widely used as a parametric tool to find an optimal structural shape of shell structures for a prescribed objective function and a given design load. However, the current optimization methods are limited to finding a geometry under only a specific static load like the dead load or an equivalent static seismic load for predefined geometrical shapes, and so can not be applied to free-form gridshells. This poses a challenge to achieving an efficient free-form shell structure in high seismic hazard areas. This paper aims to resolve this by presenting a computational morphogenesis method to obtain form-found shell structures by considering the dynamic seismic loads and the response reduction effects of seismic energy-dissipating devices using generalized response spectrum analysis. The method was applied to optimize the buckling-restrained brace layouts on target spherical metal gridshell structures with different diameter-to-height ratios. The resulting form-found structures had an efficient roof geometry, along with an efficient damper layout (to prevent member buckling and the dropout of finishing materials). Dampers were found to be more efficient if placed in the (relatively heavy) supporting structure instead of the roof, and a flattened but locally bulged roof shape proved to be the most efficient in mitigating the seismic response. The generalized response spectrum analysis significantly reduced the computation time while evaluating the displacement response with sufficient practical accuracy, although it slightly underestimates the acceleration response if compared to the conventional nonlinear response history analysis results.</p>
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		<title>Optimal Mixed Placement and Capacity Distribution of Buckling-Restrained Braces and Conventional Braces on a Large Metal Spatial Structure Without Rigid Diaphragm Assumption</title>
		<link>https://www.zawawatech.arch.ens.titech.ac.jp/optimal-mixed-placement-and-capacity-distribution-of-buckling-restrained-braces-and-conventional-braces-on-a-large-metal-spatial-structure-without-rigid-diaphragm-assumption/</link>
		
		<dc:creator><![CDATA[ZawawatechEditor]]></dc:creator>
		<pubDate>Fri, 01 Jul 2022 07:10:00 +0000</pubDate>
				<category><![CDATA[Research]]></category>
		<category><![CDATA[GRSA]]></category>
		<category><![CDATA[Seismic optimization]]></category>
		<guid isPermaLink="false">https://www.zawawatech.arch.ens.titech.ac.jp/?p=730</guid>

					<description><![CDATA[<p><img src="https://www.zawawatech.arch.ens.titech.ac.jp/wp-content/uploads/2024/08/02-3-1024x724.png" class="webfeedsFeaturedVisual" /></p>　本論文は基本計画から設計協力していた実プロジェクトの制振部材の最適設計について報告しています。寺澤が提案する最適設計アプローチを実際に適用した案件です。それまで数百自由度のモデルでワイワイ戯れていたところにいきなり数万 [&#8230;]]]></description>
										<content:encoded><![CDATA[<p><img src="https://www.zawawatech.arch.ens.titech.ac.jp/wp-content/uploads/2024/08/02-3-1024x724.png" class="webfeedsFeaturedVisual" /></p>
<figure class="wp-block-embed is-type-video is-provider-youtube wp-block-embed-youtube wp-embed-aspect-16-9 wp-has-aspect-ratio"><div class="wp-block-embed__wrapper">
<iframe title="Design of a long-span spatial structure with buckling restrained braces using spectrum analysis" width="500" height="281" src="https://www.youtube.com/embed/ankkARAjVYU?feature=oembed" frameborder="0" allow="accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share" referrerpolicy="strict-origin-when-cross-origin" allowfullscreen></iframe>
</div></figure>



<p>　本論文は基本計画から設計協力していた実プロジェクトの制振部材の最適設計について報告しています。寺澤が提案する最適設計アプローチを実際に適用した案件です。それまで数百自由度のモデルでワイワイ戯れていたところにいきなり数万自由度（実物）を耐震最適化してください，ということになり大変苦労しました。大変勉強になりました。<a rel="noreferrer noopener" href="https://doi.org/10.3389/fbuil.2022.954117" data-type="URL" data-id="https://doi.org/10.3389/fbuil.2022.954117" target="_blank"><strong>論文はこちら</strong></a></p>



<p>This paper presents a design application of the proposed generalized response spectrum analysis (GRSA)-based seismic optimization method to a large metal spatial structure (constructed in Japan) where a rigid diaphragm assumption is not available and displacement responses are disproportionally distributed in a story. It also discusses the optimal mixed placement and capacity distribution of buckling-restrained braces (BRBs) and conventional braces (CBs) to minimize both the story drift response and the number of BRBs (i.e., the introduction cost of expensive energy-dissipation devices used as dampers). GRSA is a quick and efficient analysis method for estimating the reduced seismic responses of structural models with a large degree of freedom, and GRSA-based computational optimization enables a more efficient seismic design process than trial-and-error approaches with time-consuming nonlinear response history analysis. In this study, the efficiency is verified through a comparison with the Japanese standard BRB design method. According to the results, the optimal design solution by the proposed method has approximately 20% less steel tonnage of BRBs than that obtained from the standard method, whereas the seismic performance is equal to or better than the others. Moreover, although engineers should still consider the possibility of damage concentration, the brace configuration of the substructure where BRBs and CBs are arranged in adjacent stories is the most effective for reducing both the number of BRBs and the story drift response.</p>
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		<title>一般化応答スペクトル解析法に基づく免震構造の設計手法 DESIGN METHOD OF SEISMICALLY ISOLATED STRUCTURES BASED ON GENERALIZED RESPONSE SPECTRUM ANALYSIS</title>
		<link>https://www.zawawatech.arch.ens.titech.ac.jp/%e4%b8%80%e8%88%ac%e5%8c%96%e5%bf%9c%e7%ad%94%e3%82%b9%e3%83%9a%e3%82%af%e3%83%88%e3%83%ab%e8%a7%a3%e6%9e%90%e6%b3%95%e3%81%ab%e5%9f%ba%e3%81%a5%e3%81%8f%e5%85%8d%e9%9c%87%e6%a7%8b%e9%80%a0%e3%81%ae/</link>
		
		<dc:creator><![CDATA[ZawawatechEditor]]></dc:creator>
		<pubDate>Tue, 01 Sep 2020 06:01:00 +0000</pubDate>
				<category><![CDATA[Research]]></category>
		<category><![CDATA[GRSA]]></category>
		<category><![CDATA[Seismic optimization]]></category>
		<guid isPermaLink="false">https://www.zawawatech.arch.ens.titech.ac.jp/?p=669</guid>

					<description><![CDATA[<p><img src="https://www.zawawatech.arch.ens.titech.ac.jp/wp-content/uploads/2020/09/17_sano-1024x724.png" class="webfeedsFeaturedVisual" /></p>　本研究は一般化応答スペクトル解析法を様々な免震構造の立体モデルの地震応答評価に拡張し，その上でGRSA応答値の等値線図に基づく免震構造の設計法を提案しました。論文はこちら This paper presents a d [&#8230;]]]></description>
										<content:encoded><![CDATA[<p><img src="https://www.zawawatech.arch.ens.titech.ac.jp/wp-content/uploads/2020/09/17_sano-1024x724.png" class="webfeedsFeaturedVisual" /></p>
<p>　本研究は一般化応答スペクトル解析法を様々な免震構造の立体モデルの地震応答評価に拡張し，その上でGRSA応答値の等値線図に基づく免震構造の設計法を提案しました。<strong><a href="https://doi.org/10.3130/aijs.85.1187" data-type="URL" data-id="https://doi.org/10.3130/aijs.85.1187" target="_blank" rel="noreferrer noopener">論文はこちら</a></strong></p>



<p>This paper presents a design method for highly indeterminate seismically isolated structures utilizing generalized response spectrum analysis, which has been extended to simulate both of an elasto-plastic damper with isolator and a nonlinear oil damper. This enables a more efficient design process than trial-and-error approaches with non-linear response history analysis. The design example using the proposed method are demonstrated in a series of studies using a base isolation system with a tall building and mid-story isolation or roof isolation systems having substructures with dampers.</p>
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		<title>ELASTO-PLASTIC DAMPER OPTIMIZATION ROUTINE FOR LATTICE TOWERS BASED ON GENERALIZED RESPONSE SPECTRUM ANALYSIS</title>
		<link>https://www.zawawatech.arch.ens.titech.ac.jp/elasto-plastic-damper-optimization-routine-for-lattice-towers-based-on-generalized-response-spectrum-analysis/</link>
		
		<dc:creator><![CDATA[ZawawatechEditor]]></dc:creator>
		<pubDate>Sat, 01 Dec 2018 04:59:00 +0000</pubDate>
				<category><![CDATA[Research]]></category>
		<category><![CDATA[GRSA]]></category>
		<category><![CDATA[Seismic optimization]]></category>
		<guid isPermaLink="false">https://www.zawawatech.arch.ens.titech.ac.jp/?p=624</guid>

					<description><![CDATA[<p><img src="https://www.zawawatech.arch.ens.titech.ac.jp/wp-content/uploads/2024/08/04-2-1024x724.png" class="webfeedsFeaturedVisual" /></p>　実在するトラス鉄塔の耐震改修を対象に，座屈拘束ブレースの配置と容量分布量の最適化を行い，提案する一般化応答スペクトル解析法に基づく最適設計アプローチと既存改修の有効性を比較検証しました。2018年度のHANGAI Pr [&#8230;]]]></description>
										<content:encoded><![CDATA[<p><img src="https://www.zawawatech.arch.ens.titech.ac.jp/wp-content/uploads/2024/08/04-2-1024x724.png" class="webfeedsFeaturedVisual" /></p>
<p>　実在するトラス鉄塔の耐震改修を対象に，座屈拘束ブレースの配置と容量分布量の最適化を行い，提案する一般化応答スペクトル解析法に基づく最適設計アプローチと既存改修の有効性を比較検証しました。2018年度のHANGAI Prizeとして国際・シェル空間構造学会から表彰いただき，MITで開催された年次総会で招待講演しました。それまで鼻つまみ物のような扱いを受けていた提案手法が認められるきっかけとなった論文でした。<strong><a rel="noreferrer noopener" href="https://doi.org/10.20898/j.iass.2018.198.035" data-type="URL" data-id="https://doi.org/10.20898/j.iass.2018.198.035" target="_blank">論文はこちら</a></strong></p>



<p>This paper presents a damper design routine for highly indeterminate 3-D structures utilizing computational optimization and response spectrum analysis, which has been extended to incorporate non-proportional damping. This enables a more efficient design process than trial-and-error approaches. An example retrofit of a seismically deficient lattice tower using buckling-restrained braces is presented.</p>
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		<title>一般化応答スペクトル解析法に基づく制振ブレース構造の最適設計手法 Optimal damper design strategy for braced structures based on generalized response spectrum analysis</title>
		<link>https://www.zawawatech.arch.ens.titech.ac.jp/%e4%b8%80%e8%88%ac%e5%8c%96%e5%bf%9c%e7%ad%94%e3%82%b9%e3%83%9a%e3%82%af%e3%83%88%e3%83%ab%e8%a7%a3%e6%9e%90%e6%b3%95%e3%81%ab%e5%9f%ba%e3%81%a5%e3%81%8f%e5%88%b6%e6%8c%af%e3%83%96%e3%83%ac%e3%83%bc/</link>
		
		<dc:creator><![CDATA[ZawawatechEditor]]></dc:creator>
		<pubDate>Thu, 01 Nov 2018 04:40:00 +0000</pubDate>
				<category><![CDATA[Research]]></category>
		<category><![CDATA[GRSA]]></category>
		<category><![CDATA[Seismic optimization]]></category>
		<guid isPermaLink="false">https://www.zawawatech.arch.ens.titech.ac.jp/?p=616</guid>

					<description><![CDATA[<p><img src="https://www.zawawatech.arch.ens.titech.ac.jp/wp-content/uploads/2024/08/08_OptGRSA01-1024x724.png" class="webfeedsFeaturedVisual" /></p>　本研究では，制振部材，特に弾塑性ダンパーも含む立体モデルに適用可能な応答スペクトル解析法と最適化アルゴリズムを組合せた制振構造物の設計手法の提案に基づき，様々な適用例を通してその有効性と解の特性を分析しました。一般化応 [&#8230;]]]></description>
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<p>　本研究では，制振部材，特に弾塑性ダンパーも含む立体モデルに適用可能な応答スペクトル解析法と最適化アルゴリズムを組合せた制振構造物の設計手法の提案に基づき，様々な適用例を通してその有効性と解の特性を分析しました。一般化応答スペクトル解析法に基づく最適設計アプローチの開発と実践の第二弾であり，スクリプト言語，数値解析，クラウド上の高性能計算環境(HPC)を実際に連動させて，寺澤の考えているコンピュテーショナルデザインをデモンストレーションしてみた，という研究です。EESDかEngineering Structuresに投稿しようと考えていたので，無理やり黄表紙とJARに投稿させられたことを今も後悔しています。前報から学位の先を見て動いていたので、博論とのストーリーの辻褄を合わせるのが大変でした。序文の座屈がどうとか話題がとっちらかって書いてあるのはそういう事情です。<a rel="noreferrer noopener" href="https://doi.org/10.3130/aijs.83.1689" data-type="URL" data-id="https://doi.org/10.3130/aijs.83.1689" target="_blank"><strong>日本語論文はこちら</strong></a>、<strong><a rel="noreferrer noopener" href="https://doi.org/10.1002/2475-8876.12122" data-type="URL" data-id="https://doi.org/10.1002/2475-8876.12122" target="_blank">English manuscript is here</a>.</strong></p>



<p>This paper presents an optimal damper design strategy for highly indeterminate 3D structures utilizing computational optimization and response spectrum analysis, which has been extended to incorporate non-proportional damping. This enables a more efficient design process than trial-and-error approaches with non-linear response history analysis. The efficiency of the proposed design strategy is verified, analyzed and discussed in a series of studies using an existing lattice tower structure, popular buckling-restrained braced frames and a concentric braced frame skin structure.</p>
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		<title>Generalized Response Spectrum Analysis for Structures with Dampers</title>
		<link>https://www.zawawatech.arch.ens.titech.ac.jp/generalized-response-spectrum-analysis-for-structures-with-dampers/</link>
		
		<dc:creator><![CDATA[ZawawatechEditor]]></dc:creator>
		<pubDate>Wed, 01 Aug 2018 04:11:00 +0000</pubDate>
				<category><![CDATA[Research]]></category>
		<category><![CDATA[GRSA]]></category>
		<guid isPermaLink="false">https://www.zawawatech.arch.ens.titech.ac.jp/?p=597</guid>

					<description><![CDATA[<p><img src="https://www.zawawatech.arch.ens.titech.ac.jp/wp-content/uploads/2018/08/37_terazawa-1024x549.png" class="webfeedsFeaturedVisual" /></p>　ダンパーを含む任意形状の立体モデルに適用可能な一般化応答スペ クトル解析法(Generalized Response Spectrum Analysis，GRSA)を構築し，広範なモデルパラメータ を用いた時刻歴応答解 [&#8230;]]]></description>
										<content:encoded><![CDATA[<p><img src="https://www.zawawatech.arch.ens.titech.ac.jp/wp-content/uploads/2018/08/37_terazawa-1024x549.png" class="webfeedsFeaturedVisual" /></p>
<p>　ダンパーを含む任意形状の立体モデルに適用可能な一般化応答スペ クトル解析法(Generalized Response Spectrum Analysis，GRSA)を構築し，広範なモデルパラメータ を用いた時刻歴応答解析との比較から，その評価精度，適用性，時間効率性の向上を検証しました。アメリカで色々な価値観に触れてきた結果，寺澤は博士論文の方針を大きく転換しました。原稿は英語がひどく半年経っても査読が返ってこず、難渋を極めましたが，今では私の研究テーマの大きな柱になりました。<a href="https://doi.org/10.1193/092217EQS188M" data-type="URL" data-id="https://doi.org/10.1193/092217EQS188M" target="_blank" rel="noreferrer noopener"><strong>論文はこちら</strong></a></p>



<p>In this study, a computational seismic design routine is proposed based on a generalized response spectrum analysis for highly indeterminate structures with energy-dissipation members, such as viscous or elasto-plastic dampers. Complex stiffness terms are introduced to account for displacement-dependent damping, and a three-dimensional (3-D) element stiffness matrix with complex axial stiffness is proposed for elasto-plastic dampers. A modified complete quadratic combination method previously developed for real symmetric damped systems is extended to complex asymmetric damped systems, based on a theoretical analysis of eigenvalue equations. The response is evaluated by iteratively conducting complex eigenvalue analysis and modal combination. The accuracy is confirmed through comparison to nonlinear response history analysis of 2-D frame models. Finally, an example application is presented of a 3-D truss tower seismically retrofitted by replacing the braces with viscoelastic and then elasto-plastic dampers. The proposed design routine is used to rapidly identify novel and efficient damper arrangements and sizing distributions, avoiding computationally intensive nonlinear response history analysis.</p>
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