Optimization of elastic spring stiffness distribution across floors using Nelder-Mead method to reduce collision effects in adjacent structures under seismic influence

Abstract

Context—Seismic pounding between adjacent buildings is a structural safety problem where separation gaps are limited. Differences in period, stiffness, mass and damping can produce out-of-phase motion, large relative displacement and velocity demands, and impact damage. Because widening joints is often impractical in existing building stock, connection-based control strategies are needed.

Objective—This study optimizes the floor-wise stiffness distribution of elastic links between two adjacent buildings and removes links whose optimized stiffness falls below a selected threshold.

Method—Two equal-height, ten-story shear-building models with different dynamic properties were connected at corresponding floors by passive linear springs without added damping. The coupled equations of motion were formulated, and the top-floor relative-velocity transfer-function variance under stationary random excitation was minimized using the derivative-free Nelder–Mead algorithm subject to individual and total stiffness constraints. Links contributing less than 1% of the total stiffness were removed after optimization. The final configuration was assessed by time-history analyses under 11 ground-motion records and independently verified in OpenSees. Relative displacement, relative velocity, story shear and pounding response were evaluated. The objective function was defined through the difference between the top-floor velocity transfer functions of Buildings A and B, based on the random-vibration approach. Lower and upper stiffness limits for each spring and an upper limit on total connection stiffness were imposed during optimization.

Results—The optimum stiffness distribution was highly nonuniform: 73.6% of total connection stiffness was assigned to the 10th floor and 14.9% to the 3rd floor. Links at the 1st, 4th, 7th and 9th floors fell below the threshold and were removed. Across 11 records, maximum roof-level relative displacement decreased by 91.58–97.90% and relative velocity by 77.84–97.81%; mean reductions were 96.06% and 92.76%. Under El Centro excitation, story shears decreased throughout the more flexible Building B but changed nonuniformly in Building A. The controlled model eliminated pounding for the adopted joint and contact model.

Conclusion—Optimizing and pruning floor-wise elastic links effectively reduced relative seismic response and pounding demand, although absolute force demands did not decrease uniformly in both buildings. The controlled response change arose not from an additional damping mechanism, but from the equal and opposite forces transferred by the elastic springs and the resulting change in the coupled system’s dynamic properties.

Keywords

• Adjacent buildings
• Elastic spring links
• Nelder-Mead optimization
• Random vibration
• Seismic response
• Structural pounding

Deprem etkisi altındaki bitişik nizam yapılarda çarpışma etkisinin azaltılması için katlar boyunca elastik yay rijitliği dağılımının Nelder-Mead ile optimizasyonu

Abstract

Arka Plan—Bitişik nizam yapılarda yetersiz derz boşluğu, farklı periyot, rijitlik, kütle ve sönüm özellikleri nedeniyle faz dışı hareketlere; büyük göreli deplasman ve hız taleplerine ve çarpışma hasarına yol açabilmektedir. Mevcut yapı stokunda derz genişliğinin artırılması çoğu zaman uygulanabilir olmadığından, göreli hareketi azaltan bağlantı tabanlı kontrol yöntemlerine ihtiyaç vardır.

Amaç—Bu çalışmada, farklı dinamik özelliklere sahip iki bitişik yapıyı bağlayan elastik yayların katlar boyunca rijitlik dağılımının optimize edilmesi ve optimize rijitliği belirlenen eşiğin altında kalan bağlantıların çıkarılması amaçlanmıştır.

Yöntem—Farklı dinamik özelliklere sahip, eşit yükseklikte iki on katlı kayma bina modeli, karşılıklı kat seviyelerinde ek sönüm içermeyen pasif doğrusal yaylarla bağlanmıştır. Birleşik hareket denklemleri oluşturulmuş; durağan rastgele uyarım altında tepe kat göreli hız transfer fonksiyonu varyansı, tekil ve toplam rijitlik kısıtları altında türev gerektirmeyen Nelder–Mead algoritmasıyla en aza indirilmiştir. Toplam rijitliğin %1’inden az katkı veren bağlantılar optimizasyon sonrasında çıkarılmıştır. Nihai düzen 11 deprem kaydı altında zaman tanım alanı analizleriyle değerlendirilmiş ve OpenSees modeliyle bağımsız olarak doğrulanmıştır. Göreli deplasman, göreli hız, kat kesme kuvveti ve çarpışma tepkileri incelenmiştir. Amaç fonksiyonu, rastgele titreşim yaklaşımı temel alınarak A ve B yapılarının tepe kat hız transfer fonksiyonları arasındaki fark üzerinden tanımlanmıştır. Optimizasyon sırasında her bir yay için alt ve üst rijitlik sınırları ile toplam bağlantı rijitliği üst sınırı dikkate alınmıştır.

Bulgular—Optimum dağılım düzgün değildir: toplam bağlantı rijitliğinin %73.6’sı 10. kata, %14.9’u 3. kata atanmıştır. 1., 4., 7. ve 9. katlardaki bağlantılar eşik altında kaldığı için çıkarılmıştır. On bir kayıtta tepe kat maksimum göreli deplasmanı %91.58–%97.90, göreli hızı %77.84–%97.81 azalmış; ortalama azalmalar sırasıyla %96.06 ve %92.76 olmuştur. El Centro kaydında kat kesme kuvvetleri daha esnek B yapısında tüm katlarda azalırken A yapısında düzensiz değişmiştir. Seçilen derz ve temas modeli altında kontrollü sistemde çarpışma ortadan kalkmıştır.

Sonuç—Kat bazındaki elastik bağlantıların optimize edilip düşük katkılı bağlantıların çıkarılması, göreli deprem tepkisini ve çarpışma talebini etkili biçimde azaltmış; ancak mutlak kuvvet talepleri iki yapıda aynı ölçüde azalmamıştır. Kontrollü sistemde meydana gelen tepki değişimi ek bir sönüm mekanizmasına değil, elastik yayların iki yapı arasında oluşturduğu eşit ve zıt kuvvet aktarımına ve bunun sonucunda birleşik sistemin dinamik özelliklerinde meydana gelen değişime dayanmaktadır.

Keywords

• Bitişik nizam yapılar
• Elastik yay bağlantıları
• Nelder-Mead optimizasyonu
• Rastgele titreşim
• Deprem tepkisi
• Yapısal çarpışma

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