Modifikasi Metoda Newton Raphson Nonlinear Geometri pada Sistem Struktur Rangka Sendi
DOI:
https://doi.org/10.22441/jrs.2019.V08.i1.04Keywords:
nonlinear geometr, softening, snap-through, stiffeningAbstract
Sistem nonlinier, sifat proporsionalitas gaya-perpindahan, hukum superposisi tidak berlaku, urutan pembebanan sangat berpengaruh terhadap hasil akhir tanggap struktur Tulisan ini membahas analisis struktur yang nonlinear geometri dengan kasus perpindahan yang hingga (finitesimal). Formulasi dituliskan bentuk matriks dan menggunakan model elemen hingga. Analisis struktur dituangkan dalam satu program paket komputer yang dituliskan dalam bahasa tinggi Fortran.
Analisis dilakukan dengan menerapkan teknik inkrementasi berturutan. Setiap inkrementasi beban dianalisis dengan menggunakan teknik iterasi Newton-Raphson dan Newton-Raphson modifikasi. Untuk tahap pembebanan dengan sifat struktur yang melunak maupun mengeras, diterapkan teknik iterasi Newton-Raphson. Sedangkan untuk tahap pembebanan dengan determinan matriks kekakuan global yang mendekati nol atau negatif, sebagai mana ditemukan dalam kasus snap-through, digunakan teknik iterasi Newton-Raphson namun dengan menambahkan elemen pendel sebagai dongkrak dengan kekakuan aksial yang relatif besar untuk membuat determinan matriks kekakuan menjadi positif.
Program yang disusun diuji coba terhadap struktur yang telah dianalisis dengan program paket komputer lain yang standart, dalam hal ini Structural Analysis Program (SAP). Uji coba ini merupakan verifikasi dari pada kebenaran dan ketelitian dari pada program paket yang baru disusun dan diterapkan. Program kemudian diterapkan dalam beberapa contoh studi kasus terhadap sistem struktur. Di antaranya dilakukan dengan mengambil perbandingan tinggi terhadap bentang struktur yang bervariasi dan mengambil perbandingan kekakuan aksial elemen dongkrak terhadap kekakuan aksial pendel-pendel yang bervariasi.
Hasil analisis berupa kurva beban-perpindahan untuk tiga respon struktur, yaitu softening, snap-through, dan stiffening. Perilaku nonlinear makin jelas dengan mengecilnya modulus elastisitas dan luas penampang. Makin lunak bahan, makin besar perpindahan yang terjadi untuk pembebanan yang sama. Perilaku nonlinear juga semakin terlihat pada struktur akibat pengaruh perbandingan tinggi struktur terhadap bentang. Semakin kecil perbandingan tersebut, semakin nyata pengaruh dari nonlinear geometri.
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References
Bathe, K.J., (1982) Finite Element Procedures in Engineering Analysis, Prentice Hall.
Cook, R. D., Malkus, D. S., Plesha, M. E. dan Witt, R. J., (2002) Concepts and Applications of Finite Element Analysis, John Wiley & Sons, Inc.
Cook, R. D., Bambang,S., (1990) Konsep dan Aplikasi MEtoda Elemen Hingga. Eresco Bandung.
Hariandja, B. H., (1997) Analisis Struktur Dalam Formulasi Matriks. Aksara Hutasada: Bandung.
Hariandja, B. H., (1985) Adaptive Finite Element Analysis of Nonlinear Frictional Contact with Mixed Eulerian-Lagrangian Coordinates, doctoral dissertation, Civil Engineering Department, the University of Illinois at Urbana- Champaign, USA.
Logan, D.L, (1986) A first Course in the Finite Element Method, PWS Engineeing.
Lalo, D. F., Silva, M. O., & Greco, M. (2018). Influence of damping ratio on a structural optimization design considering a dynamic analysis within the time domain. Acta Scientiarum. Technology, 40.
Li, G., & Yu, D. H. (2018). Efficient Inelasticity-Separated Finite-Element method for material nonlinearity analysis. Journal of Engineering Mechanics, 144(4), 04018008.
Mahmul, Mariatul K.,. (2017) Yudhi Modifikasi Metode Newton-Raphson Untuk Mencari Solusi Persamaan Linear Dan Nonlinear
Muin, R.B. (2010) Pemodelan Gerak Dinamik Struktur Yang Berinteraksi Dengan Tanah Nonliniear Pada Arah Horizontal, KNPTS-ITB, Bandung. ISBN 978-979-16225-5-4.
Muin, R.B. (2010) Nonlinear Response of Soil-Structure-Interaction due to Cyclic Loading, 1-ICSBE (UII), Indonesia, ISBN 9780979-96122-9-8.
Nasution A, Metoda Elemen Hingga, ITB: Bandung (2010)
Nasution A, Zakaria H. Metode Numerik Dalam Ilmu Rekayasa Sipil. ITB: Bandung (2001)
Putri, L.A., Handayanu., Budi, E. D. (2014) Analisa Struktur Dengan Metode Elemen Hingga Nonlinear (SNTMUT – 2014)
Weaver, J.R. and Johnston, P.R., Finite Element for Structural Analysis, Prentice, (1987)
Zienkiewicz, O. C., Taylor. R. L., The Finite Element Method, Volume 1 & 2, McGraw-Hill, (1989,1991)
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