Design and Thermal Elastic Behavior of FGM Sandwich Plate with TPMS Core Layer

Öz

This study examines the thermo-mechanical behavior of a sandwich plate with functionally graded (FGM) face sheets and a TPMS core. The faces are made of Si₃N₄/SUS304 and follow a power-law distribution. The Primitive, Gyroid, and IWP TPMS structures are modeled through homogenized Gibson–Ashby relations. Temperature-dependent elastic and thermal properties are included for all layers. The analysis focuses on how the material grading index, temperature rise, and TPMS volume fraction change the equivalent in-plane elastic modulus and equivalent bending elastic modulus of the sandwich plate. In a homogeneous solid plate, the in-plane (membrane) and bending responses are uncoupled and governed by uniform stiffness through the thickness. In contrast, plates with a compliant core, such as sandwich structures, exhibit different effective membrane and bending elasticities due to the non-uniform stiffness distribution across the thickness. These two properties govern the global in-plane and flexural behavior. Results show that both elasticities decrease strongly with temperature. Higher grading index also softens the structure, since the metal-rich region becomes more dominant at elevated temperature. The study also shows that the TPMS core plays a major role. A higher TPMS filling ratio increases membrane stiffness and raises bending rigidity. At the same time, Poisson’s ratio becomes smaller, and thermal conductivity decreases as the core becomes more porous. Thermal expansion is influenced mainly by the grading index. Benchmark comparisons confirm the accuracy of the present model. The predicted thermal buckling temperatures agree well with previous higher-order theories. The study provides trends for how temperature, gradation, and TPMS architecture jointly shape membrane and bending elasticity.

Anahtar Kelimeler

• Sandwich plate
• TPMS
• FGM
• Material Properties

Etik Beyan

The author of this article declares that the materials and methods they use in their work do not require ethical committee approval and/or legal-specific permission.

TPMS Çekirdek Katmanlı FDM Sandviç Plakanın Tasarımı ve Termo Elastik Davranışı

Öz

Bu çalışma, fonksiyonel olarak derecelendirilmiş (FDM) yüzey tabakalarına ve TPMS çekirdeğe sahip bir sandviç plakanın termo-mekanik davranışını incelemektedir. Yüzey tabakaları Si₃N₄/SUS304 malzemelerinden oluşmakta ve güç yasasına dayalı bir dağılım izlemektedir. Primitive, Gyroid ve IWP TPMS yapıları, homojenleştirilmiş Gibson–Ashby ilişkileri kullanılarak modellenmiştir. Tüm tabakalar için sıcaklığa bağlı elastik ve termal malzeme özellikleri dikkate alınmıştır. Analiz, malzeme derecelendirme indeksi, sıcaklık artışı ve TPMS hacim doluluk oranının sandviç plakanın efektif membran elastisite modülü ve efektif eğilme elastisite modülü üzerindeki etkilerine odaklanmaktadır. Homojen tek katmanlı bir plakada, düzlem içi (membran) ve eğilme tepkileri birbirinden bağımsızdır ve kalınlık boyunca bir rijitlik dağılımı tarafından belirlenir. Buna karşılık, sandviç yapılar gibi daha yumuşak bir çekirdeğe sahip plakalarda, kalınlık boyunca rijitliğin düzgün olmaması nedeniyle etkin membran ve eğilme elastisite modülleri birbirinden farklılaşmaktadır. Bu iki elastik özellik, yapının genel düzlem içi ve eğilme davranışını belirlemektedir. Sonuçlar, her iki elastisite modülünün de sıcaklık arttıkça belirgin şekilde azaldığını göstermektedir. Malzeme derecelendirme indeksinin artması da, yüksek sıcaklıklarda metal ağırlıklı bölgenin baskın hâle gelmesi nedeniyle yapının yumuşamasına yol açmaktadır. Çalışma ayrıca TPMS çekirdeğin belirleyici bir rol oynadığını ortaya koymaktadır. TPMS doluluk oranının artması, membran rijitliğini artırmakta ve eğilme rijitliğini yükseltmektedir. Aynı zamanda, çekirdek daha boşluklu hâle geldikçe Poisson oranı azalmakta ve ısıl iletkenlik düşmektedir. Isıl genleşme ise esas olarak malzeme derecelendirme indeksinden etkilenmektedir. Doğrulama çalışmaları, sunulan modelin doğruluğunu teyit etmektedir. Hesaplanan termal burkulma sıcaklıkları, daha önce geliştirilen yüksek mertebeli teorilerle iyi bir uyum göstermektedir. Bu çalışma, sıcaklık, derecelendirme indeksi ve TPMS geometrisinin birlikte membran ve eğilme rijitliklerinden kaynaklanan elastisite modüllerinin nasıl şekillendirdiğine dair genel eğilimleri ortaya koymaktadır.

Anahtar Kelimeler

• Sandviç plaka
• TPMS
• FDM
• Malzeme özellikleri

Etik Beyan

Bu makalenin yazarı çalışmalarında kullandıkları materyal ve yöntemlerin etik kurul izni ve/veya yasal-özel bir izin gerektirmediğini beyan ederler.

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