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A new four‐node (non‐flat) general quadrilateral shell element for geometric and material non‐linear analysis is presented. The element is formulated using three‐dimensional continuum mechanics theory and it is applicable to the analysis of thin and thick shells. The formulation of the element and the solutions to various test and demonstrative example problems are presented and discussed.

The primitive variable finite element formulation is used in a straightforward manner to solve for two turbulent pipe flows. The solution is based on the use of the Nikuradse—van Driest mixing‐length formula but no special wall element is employed. The finite element solutions are compared with experimental results.

We describe a visual method—stress band plots—for displaying the stress solution within a two‐dimensional finite element mesh. The stress band plots differ from conventional stress contour plots because stress band plots display unaveraged stresses (the stresses are computed directly from the solution variables) and stress discontinuities in the finite element solution are directly displayed. Stress band plots are useful in judging the accuracy of a finite element solution, in the comparison of different finite element solutions and during mesh refinement. These uses are demonstrated in an axisymmetric pressure vessel analysis.

An infinite element based on the doubly asymptotic approximation (DAA) for use in finite element analysis of fluid—structure interactions is presented. Fluid finite elements model the region near the solid. Infinite elements account for the effects of the outer fluid on the inner region. The DAA‐based infinite elements involve an approximate calculation of the added mass using static mapped infinite elements, plus a consistent damping term. Simple test analyses for a range of fluid properties demonstrate the performance of the solution technique. The analyses of a Helmholtz resonator (open pipe) and a circular plate in water indicate the practical use of the solution approach.

We briefly summarize the theoretical formulations of our MITC plate bending elements and then present numerical convergence results. The elements are based on Reissner‐Mindlin plate theory and a mixed‐interpolation of the transverse displacement, section rotations and transverse shear strain components. We consider our 4, 9 and 16‐node quadrilateral elements and our 7 and 12‐node triangular elements. The theoretical and numerical results indicate the high reliability and effectiveness of our elements.

Computational efficiency and reliability are clearly the most important requirements for the success of a meshless numerical technique. While the basic ideas of meshless techniques are simple and well understood, an effective meshless method is very difficult to develop. The efficiency depends on the proper choice of the interpolation scheme, numerical integration procedures and techniques of imposing the boundary conditions. These issues in the context of the method of finite spheres are discussed.

The kinematics of small and large deformations (displacements, rotations and strains) is described by use of the engineering strain, the logarithmic strain, the Seth‐Hill class of strains and the rate‐type strains derived using the Lagrangian and the ‘Relative’ descriptions. The displacement gradient is computed for two and three dimensions and the error associated with use of the small rotation approximation is plotted. The components of the rotation tensor are derived for a four‐noded isoparametric quadrilateral finite element for determining the error due to small displacement and rotation approximations. Finally, the various strain measures are computed and plotted for representative problems.

The main aim of this study is to determine the fracture toughness and accordingly to predict the fracture initiation, crack propagation and mode of crack extension accurately in polypropylene subsea pipes subjected to internal pressure.

Tensile test was performed following the ISO 527–1 standard. An elastic-plastic constitutive model was developed based on the tensile test results, and it is implemented in the FEA model to describe the constitutive behaviour of the polypropylene material. Three-point bend tests with linear-elastic fracture mechanics (LEFM) approach were conducted following ISO-13586 standard, from which the average fracture toughness of the polypropylene pipe material in crack-opening mode was found as KIc = 3.3 MPa√m. A numerical model of the experiments is developed based on the extended finite element method (XFEM), which showed markedly good agreement with the experimental results.

The validated XFEM modelling approach is utilised to illustrate its capabilities in predicting fracture initiation and crack propagation in a polypropylene subsea pipe subjected to an internal pressure containing a semi-elliptical surface crack, which agrees well with existing analytical solutions. The XFEM model is capable of predicting the crack initiation and propagation in the polypropylene pipe up to the event of leakage.

The methodology proposed herein can be utilised to assess the structural integrity and resistance to fracture of subsea plastic pipes subjected to operational loads (e.g. internal pressure).

This is an attempt to better bridge the gap between the mathematical and the engineering/physical aspects of the topic. The authors trace the different sources of non-convexification in the context of topology optimization problems starting from domain discretization, passing through penalization for discreteness and effects of filtering methods, and end with a note on continuation methods.

Starting from the global optimum of the compliance minimization problem, the authors employ analytical tools to investigate how intermediate density penalization affects the convexity of the problem, the potential penalization-like effects of various filtering techniques, how continuation methods can be used to approach the global optimum and how the initial guess has some weight in determining the final optimum.

The non-convexification effects of the penalization of intermediate density elements simply overshadows any other type of non-convexification introduced into the problem, mainly due to its severity and locality. Continuation methods are strongly recommended to overcome the problem of local minima, albeit its step and convergence criteria are left to the user depending on the type of application.

In this article, the authors present a comprehensive treatment of the sources of non-convexity in density-based topology optimization problems, with a focus on linear elastic compliance minimization. The authors put special emphasis on the potential penalization-like effects of various filtering techniques through a detailed mathematical treatment.

This paper aims to present experimental and numerical analyses of fused filament fabrication (FFF) printed parts and show how mechanical characteristics of printed ABS-MG94 (acrylonitrile butadiene styrene) are influenced by the void volume fraction, cooling rate and residual thermal stresses.

Printed specimens were experimentally tested to evaluate the mechanical properties for different printing speeds, and micrographs were taken. A thermo-mechanical finite element model, able to simulate the FFF process, was developed to calculate the temperature fields in time, cooling rate and residual thermal stresses. Finally, the experimental mechanical properties and the microstructure distribution could be explained by the temperature fields in time, cooling rate and residual thermal stresses.

Micrographs revealed the increase of void volume fraction with the printing speed. The variations on voids were associated to the temperature fields in time: when the temperatures remained high for longer periods, less voids were generated. The Young's Modulus of the deposited filament varied according to the cooling rate: it decreased when the cooling rate increased. The influence of the residual thermal stresses and void volume fraction on the printed parts failure was also investigated: in the worst scenarios evaluated, the void volume fraction reduced the strength in 9 per cent, while the residual thermal stresses reduced it in 3.8 per cent.

This work explains how the temperature fields can affect the void volume fraction, Young's Modulus and failure of printed parts. Experimental and numerical results are shown. The presented research can be used to choose printing parameters to achieve desired mechanical properties of FFF printed parts.