Behavior of beam on elastic foundation using element free Galerkin method

One of mesh free methods, element free Galerkin method, is presented to analyze the finite beam on elastic foundation. The shape functions are constructed by using the moving least square interpolation based on a set of nodes that are arbitrarily distributed in specified domain. Discrete system equations are derived from the variation form of system equations. Numerical examples of finite beam on elastic foundation are given by establishing Matlab code. The results of this paper demonstrate the effectiveness of the proposed method with small errors compared to analytical solutions. Keywords: mesh free method, element free Galerkin method, moving least square, finite beam, elastic foundation.

Evaluasi Kekuatan Rel UIC54 Menggunakan Metode Beam On Elastic Foundation (BOEF)

Di Indonesia, dimensi profil baja rel telah ditentukan dalam Peraturan Menteri Perhubungan No. 60 tahun 2012. Salah satu jenis rel yang umum digunakan untuk jalan rel dengan lebar 1067mm adalah rel tipe UIC54. Namun, penentuan tipe profil rel di Indonesia belum dilengkapi dengan analisis kekuatan struktur profil rel dalam menahan beban yang bekerja di atasnya. Sehingga, jurnal ini akan membahas perhitungan analisis kekuatan struktur rel UIC54 dalam menahan beban lokomotif CC 203, CC 205, dan CC 206. Metode perhitungan menggunakan metode Beam on Elastic Foundation (BOEF) yang mengasumsikan perilaku rel sebagai balok kontinu yang menerima beban di atas tumpuan pondasi elastis. Nuilai kekuatan rel UIC dituliskan dalam bentuk angka faktor keamanan (SF). Hasil perhitungan menunjukkan bahwa nilai SF terkritis rel dalam menerima beban lokomotif CC 203, CC 205, dan CC 206 berturut-turut adalah sebesar 10,94; 8,93; dan 9,67. Berdasarkan hasil perhitungan kekuatan rel tersebut, rel UIC54 sangat kuat dalam menahan beban dinamis lokomotif dan memiliki penampang yang terlalu besar untuk menahan beban roda dinamis lokomotif.

Vehicle Load Distribution Under Timber Mats and Flexible Slab

Pipeline operators commonly use means of temporary crossing such as timber-mat, airbridge, and slab to reduce surface loading induced stresses in a buried pipeline at locations where a heavy vehicle crosses the buried pipeline. When a temporary crossing has a continuous contact with soil, (e.g. timber mat, flexible slab) load distribution over the ground surface is not immediately known. Load distribution under a timber-mat or flexible slab is a function of the slab to soil stiffness ratio. The load distribution tends to become more uniform with increasing timber-mat or slab stiffness. In this work an analytical model using beam-on-elastic-foundation has been developed and Laplace transform has been utilized to find the solution and apply free-end boundary conditions. The analytical solution can be used for any arbitrary load distribution over a beam-on-elastic foundation. In this work the solution for a point load and a partially distributed uniform load were employed as these scenarios can accurately represent conventional vehicle foot-prints, while being computationally efficient. The analytical solutions are compared to finite element analysis to validate the model. This model can be used in conjunction with the Canadian Energy Pipeline Association (CEPA) surface loading calculator (or similar tools) to analyze pipeline encroachment problems when means of temporary crossing is installed. This model can help the operators determine dimensions and bending stiffness of timber-mat or flexible slab to assure a desirable load distribution will be achieved. The model can also be used for structural analysis of a timber-mat or flexible slab under vehicular load.