The Use of Mixed Eulerian-Lagrangian Displacement in Geometrically Nonlinear Analysis of Structural System

Abstract

Abstract

The paper deals with the use of mixed Eulerian-Lagrangian displacement in geometrically nonlinear analysis of structural system, in which displacement and deformation are observed from a selected referential configuration, i.e., a configuration once occupied by the system along the loading process. The displacement measured from initial configuration into referential configuration is referred to as Eulerian displacement, and the displacement measured from referential configuration into current configuration is referred to as Lagrangian displacement. Geometrical nonlinearity of structure occurs when the displacement primarily consists of rigid body displacement, in which the choice in referential configuration is of great concern. The same deformation may be observed differently according to the choice in referential configuration. Analysis of continuum system is cast in finite element method and written in matrix formulation. The geometrical nonlinearity is approached by successive incremental steps in which the total loading is divided into several incremental loadings. The process is then linearized and incremental global stiffness matrix is used at every iteration step. The proposed mixed displacement is cast in a computer package program using Fortran language. The program is applied in several structural analysis, in which the conventional Lagrangian displacement may not be appropriate to model the analysis.

Abstrak

Makalah membahas penerapan perpindahan campuran Euler-Lagrange dalam analisis nonlinier geometri sistemstruktur, dalam mana perpindahan dan deformasi diamati dari konfigurasi referensi yang dipilih, yaitu konfigurasiyang pernah dilalui oleh sistem selama proses pembebanan. Perpindahan yang diukur dari konfigurasi awal kekonfigurasi referensi dinamakan perpindahan Euler, dan perpindahan yang diukur dari konfigurasi referensi kekonfigurasi akhir dinamakan perpindahan Lagrange. Nonlinieritas geometri sistem struktur terjadi dalam kasus dimana perpindahan terutama mencakup perpindahan badan kaku, dalam mana pemilihan konfigurasi referensimenjadi suatu langkah penting. Deformasi yang sama dapat diamati berlainan seturut dengan pilihan konfigurasireferensi. Analisis sitem kontinu didekati dengan langkah inkremental berturutan dalam mana beban total dibagiatas beberapa beban inkremental. Proses kemudian dilinierisasi dan matriks kekakuan global inkrementaldigunakan pada setiap langkah iterasi. Perpindahan campuran yang diusulkan dituangkan dalam program paketkomputer yang dituliskan dalam bahasa Fortran. Program diterapkan dalam analisis beberapa sistem struktur,dalam mana perpindahan Lagrange konvensional tidak cukup untuk memodelkan perpindahan dalam analisis.