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"ABSTRAKPenelitian ini membandingkan konvergensi elemen pelat lentur triangular yaitu MITC3, DKMT, DST-BL, dan DST-BK. Keempat elemen tersebut sama-sama memiliki 9-derajat kebebasan namun dengan formulasi regangan lentur dan regangan geser yang berbeda. Masing-masing elemen akan diuji pada beberapa kasus homogen isotrop, yaitu kasus pelat bujursangkar, pelat melingkar, pelat Razzaque, dan pelat Morley, dengan berbagai variasi ketebalan dan mesh. Keluaran uji numerik pelat homogen isotrop yang dibandingkan berupa perpindahan, momen arah-x dan momen arah-y, serta energi. Selain kasus homogen isotrop, masing-masing elemen diuji pada kasus komposit, yaitu berupa uji dari Srinivas. Dari keempat elemen yang diuji, elemen MITC3 memiliki tingkat konvergensi yang lebih lambat dibandingkan dengan elemen lainnya. Dari segi waktu komputasi, elemen MITC3 dan DKMT memiliki waktu komputasi yang lebih singkat dibandingkan dengan elemen DST-BL dan DST-BK.

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ABSTRACTThis research compare the convergence of triangular plate bending element MITC3, DKMT, DST BL, and DST BK. These elements has 9 degrees of freedom with different formulation for bending strain and shear strain interpolation. Each element is tested for several benchmark problem of isotropic condition square plate problem, circular plate problem, Razzaque skew plate, and Morley plate. The output of homogen isotropic problem is vertical displacement, moment in x direction, moment in y direction, and energy. For composite condition, numerical test is conducted for Srinivas test. In most benchmark test, MITC3 has slower convergence compared with the other elements. But on the other side, MITC3 and DKMT elements have relatively short computational time compared with DST BL and DST BK. "

"ABSTRACTThe formulation of four quadrilateral plate bending elements based of reissner. Mindlin plate theory are presented and compared. The elements are based on the modified Hellinger-Reissner mixed, on assumed shear strain fields and on the Discrete Kirchhof Mindlin Theory. Numerical results are dealing with the stability of the models, the constant patch-tests, the shear locking possibility and the convergence for benchmark problems."

"Salah satu metode pemulihan solusi gaya dalam metode elemen hinggayang paling baru adalah metode Polynomial Preserving Recovery (PPR) yang diperkenalkan oleh Zhang (2004). Metode PPR merupakan metode pemulihan superconvergent dengan menggunakan patch sebagai media perhitungan seperti yang juga digunakan dalam metode Superconvergent Patch Recovery (SPR) yang sudah lebih dulu dikenal sebagai metode pemulihan dengan kinerja bagus.Uji numerik implementasi metode tersebut perlu dilakukan dalam mengestimasi error metode elemen hingga untuk pelat lentur dengan elemen MITC. Dalam penelitian ini uji numerik akan dilakukan dengan penghalusan jaringan elemen (mesh) tipe-h secara seragam dan adaptif. Hasil pengujian tersebut akan dibandingkan dengan tiga metode pemulihan gaya dalam lainnya yaitu metode SPR, metode REP, metode rata-rata langsung, dan metode proyeksi.Program utama yang akan digunakan dalam penelitian ini untuk melakukan uji numerik dimaksud adalah program UI-FEAP yang telah disertai subrutin formulasi elemen MITC dan Error Estimator Z2 yang ditulis dalam bahasa FORTRAN hasil penelitian peneliti lain sebelumnya. Penulis menambahkan subrutin yang terkait dengan perhitungan metode PPR.

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One of the newly-published recovery methods in finite element method is the Polynomial Preserving Recovery (PPR) introduced by Zhang (2004). It is a superconvergent recovery method using patch as recovery media as done by Superconvergent Patch Recovery (SPR), which has been well known as a good recovery method.

A numerical study of the implementation of this method shall be carried out to estimate error in finite element analysis using MITC element. In this research, the numerical study will be performed by both uniform and adaptive h type mesh refinement. The result will be compared with three other recovery methods, i.e. SPR method, REP method, averaging method, and projection method. The main program to be used in the numerical study will be the UI-FEAP program, which has been enriched with MITC and Z2 error estimator subroutines written in FORTRAN programming language by other researchers. The subroutines related to PPR method shall be added in this regard.;One of the newly-published recovery methods in finite element method is the Polynomial Preserving Recovery (PPR) introduced by Zhang (2004). It is a superconvergent recovery method using patch as recovery media as done by Superconvergent Patch Recovery (SPR), which has been well known as a good recovery method.

A numerical study of the implementation of this method shall be carried out to estimate error in finite element analysis using MITC element. In this research, the numerical study will be performed by both uniform and adaptive h type mesh refinement. The result will be compared with three other recovery methods, i.e. SPR method, REP method, averaging method, and projection method. The main program to be used in the numerical study will be the UI-FEAP program, which has been enriched with MITC and Z2 error estimator subroutines written in FORTRAN programming language by other researchers. The subroutines related to PPR method shall be added in this regard."