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Abstract: An alternative formulation to current meshes dealing with finite shell elements is presented to solve the problem of stress analysis of curved pipes subjected to in-plane bending forces. The solution is based on finite curved elements, where displacements are defined from a total set of trigonometric functions or a fifth-order polynomial, combined with Fourier series. Global shell displacements are achieved through the one associated with curved arch bending and the other referred to the toroidal thin-walled shell distortion. Beam-type displacement and in-plane rotation are uncoupled and separately formulated, using trigonometric shape functions, as in Timoshenko or Mindlin beam theory. To build up the solution, a simple deformation model was adopted, based on the semi-membrane concept of the doubly curved shells behaviour. Several studies are presented and compared with experimental and numerical analyses reported by other authors. [Copyright &y& Elsevier]

Abstract: It is presented an alternative formulation to solve the problem of the deformation analysis for tubular element under pinching loads. The solution is based on a new displacement field defined from a total set of trigonometric functions. The solution is developed in a multi-nodal finite tubular ring element with a total of eight degrees of freedom per section considered. The purpose of this paper is to provide an easy alternative formulation when compared with a complex finite shell element or beam element analysis for the same application. Several case studies presented have been compared and discussed with numerical analyses results reported by other authors and the results obtained with a shell element from a Cosmos/M® programme. [Copyright &y& Elsevier]

Abstract: This work presents the development of two different finite piping elbow elements with two nodal tubular sections for mechanical analysis. The formulation is based on thin shell displacement theory, where the displacement is based on high-order polynomial or trigonometric functions for rigid-beam displacement, and uses Fourier series to model warping and ovalization phenomena of cross-tubular section. To model the internal pressure effect an additional formulation is used in the elementary stiffness matrix definition. Elbows attached to nozzle or straight pipes produce a stiffening effect due to the restraint of ovalization provided by the adjacent components. When submitted to any efforts, the excessive oval shape may reduce the structural resistance and can lead to structural collapse. For design tubular systems it is also important to consider the internal-pressure effect, given its effect on the reduction of the pipe flexibility. Some conclusions and examples are compared with results produced by other authors. [Copyright &y& Elsevier]

Abstract: The temperature, the deformation and the stress field in thermo-mechanical problems play a very important role in engineering applications. This paper presents a finite element algorithm developed to perform the thermal and mechanical analysis of structural steel piping systems subjected to elevated temperatures. The new pipe element with 22 degrees of freedom has a displacement field that results from the superposition of a beam displacement, with the displacement field associated with the section distortion. Having determined the temperature field, the consequent thermal displacement produced in the piping systems due to the thermal variation can be calculated. The temperature rise produces thermal expansion and a consequent increase of pipe length in the structural elements. For small values of the ratio of the pipe thickness to mean radius, the thermal behaviour can be calculated with adequate precision using a one-dimensional mesh approach, with thermal boundary conditions of an axisymmetric type across the pipe section. With this condition, several case studies of piping systems subjected to elevated temperatures and mechanical loads are presented and compared with corresponding results from commercial finite element codes. The main advantage of this formulation is associated with reduced time for mesh generation with a low number of elements and nodes. Considerable computational effort may be saved with the use of this finite pipe element. [Copyright &y& Elsevier]

Piping systems are structural sets used in the chemical industry, conventional or nuclear power plants and fluid transport in general-purpose process equipment. They include curved elements built as parts of toroidal thin-walled structures. The mechanical behaviour of such structural assemblies is of leading importance for satisfactory performance and safety standards of the installations. This paper presents a semi-analytic formulation based on Fourier trigonometric series for solving the pure bending problem in curved pipes. A pipe element is considered as a part of a toroidal shell. A displacement formulation pipe element was developed with Fourier series. The solution of this problem is solved from a system of differential equations using mathematical software. To build-up the solution, a simple but efficient deformation model, from a semi-membrane behaviour, was followed here, given the geometry and thin shell assumption. The flexibility factors are compared with the ASME code for some elbow dimensions adopted from ISO 1127. The stress field distribution was also calculated. [Copyright &y& Elsevier]