Computational analysis of multi-stepped beams and beams with linearly-varying heights implementing closed-form finite element formulation for multi-cracked beam elements

The use of dimensional analysis and dimensionless parameters is very common in the field of heat transfer; nevertheless the concept of non-dimensional finite element formulation has been applied to a limited type of thermo-fluid problems. The non-dimensional finite element method should provide the dimensionless solution for a given problem. The aim of present work is to develop a non-dimensional thermal finite element for getting dimensionless solution of the problems that do not have a closed form solution. An example is a fin (or extended surface) design. Fin efficiency is a performance characteristic that can be used as design criterion; thus closed form dimensionless solutions for fin efficiency are available in the literature. The results are for different geometry, single material fins. In case, if the fin problem has some geometric and/or material complexities then closed form solutions are not available and finite element approach can be used. However, the obtained finite element solution would not be in dimensionless form. For example, no closed form solutions are available for variable thickness composite fins (i.e. a fin having a base material with a coating over its surface), and the literature shows that finite element solution has been used to study thermal performance of the variable thickness composite fins. Therefore, non-dimensional finite element approach can be applied to directly obtain the dimensionless solution for the problem. The current work consists of presenting a non-dimensional finite element formulation for thermal problems. The element formulation is first validated by solving a test case study that has known closed form solution. The objective is to demonstrate the usefulness of the non-dimensional finite element approach by obtaining dimensionless finite element solutions for some applied problems that do not have a closed form solution.

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Laying Modeling of Submarine Pipelines Using Contact Elements into a Corotational Formulation

Journal of Offshore Mechanics and Arctic Engineering ◽

10.1115/1.1555117 ◽

2003 ◽

Vol 125 (2) ◽

pp. 145-152 ◽

Cited By ~ 3

Author(s):

Cora E. Marti´nez ◽

Rau´l Goncalves

Keyword(s):

Finite Element ◽

Finite Element Formulation ◽

Element Formulation ◽

Submarine Pipeline ◽

Corotational Formulation ◽

Nonlinear Beam ◽

Sea Floor ◽

Beam Elements ◽

Oil Transportation ◽

Spring Contact

A new finite element formulation to analyze stresses and displacements in submarine pipelines during laying operations is presented in this paper. The method is based on the corotational formulation using Bernoulli nonlinear beam elements to model the large displacements and rotations of the pipeline. The penalty method is used with spring-contact elements to accurately represent the actual boundary conditions on both the stinger and the sea floor. A comparison with a finite element formulation introduced by the authors in a previous paper is presented in order to verify the accuracy and computational effectiveness of the proposed method. A real laying case of an oil transportation submarine pipeline is also presented at the end of the paper to validate the results obtained with the developed formulation.

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A Simple and Efficient Large-Displacement Formulation for Beam Elements

ASME 1991 Computers in Engineering Conference: Volume 2 — Finite Elements/Computational Geometry; Computers in Education; Robotics and Controls ◽

10.1115/cie1991-0109 ◽

1991 ◽

Author(s):

Xiaodong Tang

Keyword(s):

Finite Element ◽

Closed Form ◽

Stiffness Matrix ◽

Second Order ◽

Small Displacement ◽

Element Formulation ◽

Beam Elements ◽

The Matrix ◽

Element Approach ◽

Additive Relation

Abstract A simple and effective finite element formulation of beam-column stiffness matrix with the consideration of second-order displacement is presented. The derived second-order stiffness matrix is the simple addition of the small-displacement stiffness matrix and a few other component matrices. The matrix is derived closed form and no integration is necessary during the formation of the element stiffness matrix. The simple additive relation makes it easy to understand the composition of the second-order stiffness matrix and the meaning of each component matrix. The closed-form formulation eliminates the potential numerical error and considerably reduces the amount of computation thereby, increasing the computing speed. The standard finite element approach presented in this paper makes the beam-column compatible with other finite elements and can be incorporated into existing finite element programs with little modification. The analysis of a simply supported beam with axial restraints using the beam-column element shows a good correlation with the test results.

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