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The purpose of this paper is to present an adaptive binary-tree element subdivision method (BTSM) for the evaluation of nearly singular integrals in three-dimensional boundary element method, which can facilitate automatic and high-quality patch generation.

In this method, the nearly singular element is split into two sub-elements. Each sub-element is then examined to determine if it is to be subdivided based on a specific subdivision criterion. The specific subdivision ensures that those sub-elements far from the source point are sparse. And then those sub-elements in close proximity to the source point are replaced by regular triangular elements.

With the proposed method, the sub-elements obtained are automatically refined as they approach the projection point, and they are “good” in shape and size for standard Gaussian quadrature. Thus, the proposed method can be used to evaluate nearly singular integrals accurately for cases of different element shapes and various locations of the source point.

Numerical examples for surface elements with various relative locations of the source point are presented. The results demonstrate that the proposed method has much better accuracy and robustness than some other methods.

This paper aims to propose a consistent approach to geometric modeling of optimized lattice structures for additive manufacturing technologies.

The proposed method applies subdivision surfaces schemes to an automatically defined initial mesh model of an arbitrarily complex lattice structure. The approach has been developed for cubic cells. Considering different aspects, five subdivision schemes have been studied: Mid-Edge, an original scheme proposed by the authors, Doo–Sabin, Catmull–Clark and Bi-Quartic. A generalization to other types of cell has also been proposed.

The proposed approach allows to obtain consistent and smooth geometric models of optimized lattice structures, overcoming critical issues on complex models highlighted in literature, such as scalability, robustness and automation. Moreover, no sharp edge is obtained, and consequently, stress concentration is reduced, improving static and fatigue resistance of the whole structure.

An original and robust method for modeling optimized lattice structures was proposed, allowing to obtain mesh models suitable for additive manufacturing technologies. The method opens new perspectives in the development of specific computer-aided design tools for additive manufacturing, based on mesh modeling and surface subdivision. These approaches and slicing tools are suitable for parallel computation, therefore allowing the implementation of algorithms dedicated to graphics cards.

Irregularly shaped architectural designs with surfaces curved in multiple directions, known as free-form designs, have gained significant public interest in recent decades. However, it is challenging to convert complex designs into real structures. This paper aims to realize free-form construction by developing a novel workflow in which additively manufactured thermoplastic polyurethane (TPU) molds are used.

The workflow is developed through mechanical tests on additively manufactured TPU specimens, determination of TPU mold design criteria and exploration of mold preparation methods. Two concrete elements with free-form geometries are fabricated using the proposed workflow.

TPU is a thermoplastic elastomer that is strong and inexpensive, making it an ideal mold material for casting complex concrete structures. An innovative workflow is developed in which TPU molds are used, appropriate release agents are selected for different concrete casting conditions and a mold subdivision method is proposed to facilitate the demolding process. Furthermore, the integrity of TPU molds can be maintained by following the proposed workflow, enabling repetitive use of molds. The fabrication of the two free-form structures shows that complex concrete members with high dimensional accuracy and excellent surface quality can be manufactured using the proposed method.

To the best of the authors’ knowledge, this is the first systematic study on using additively manufactured TPU molds for concrete casting of complex structures. The new techniques developed in this research can be applied to large-scale architectural, engineering and construction projects.

A new mesh generation procedure is suggested for the generation of 2D adaptive finite element meshes with strong element gradation and stretching effects. Metric tensors are employed to define and control the element characteristics during the mesh generation process. By using the metric tensor specification and a new, robust and refined advancing front triangulation kernel, triangles with nearly unit edge length with respect to the normalized space are generated. Highly graded and stretched elements can be generated without much difficulty and the operation complexity of the mesh generation process is exactly the same as the usual 2D advancing front mesh generator. A set of mesh quality enhancement procedures has also been suggested for the further improvement of the quality of the finite element meshes. A simple and effective mesh conversion scheme is used to convert the output triangular mesh to a pure quadrilateral mesh while all the essential element characteristics are preserved. Mesh generation examples show that high quality finite element meshes with element characteristics compatible with the specified metric tensors are generated within a reasonable time limit in a common small computing environment.

In order to obtain visually appealing simulation results with smooth cloth surfaces, high resolution meshes are required. Since cloth simulation with high resolution meshes is very time consuming, subdivision of a reusable model is preferred. The purpose of this paper is to adopt an approach for the subdivision of a reusable model, using different subdivision methods.

In order to obtain visually pleasing reusable garment model, the authors subdivide the model after the conversion to reusable garment model. Two meshes are employed, of which the coarse mesh is used to convert to deformable model while the subdivided mesh, i.e. the refined mesh, is for pleasing modeling results. The modified loop subdivision and modified butterfly subdivision scheme is adopted for the optimization of determining which is more suitable for the reusable model. The authors adopt an algorithm for resolving the collisions happened after the subdivision.

A 3D reusable garment model obtained from previous work was tested. The experimental results validate this method as a useful and effective approach to resolve collisions after the subdivision process.

The paper presents an approach for the subdivision of a reusable model, using different subdivision methods.

The purpose of this paper is to preset a spherical element subdivision method for the numerical evaluation of nearly singular integrals in three-dimensional (3D) boundary element method (BEM).

In this method, the source point is first projected to the tangent plane of the element. Then two cases are considered: the projection point is either inside or outside the element. In both cases, the element is subdivided into a number of patches using a sequence of spheres with decreasing radius.

With the proposed method, the patches obtained are automatically refined as they approach the projection point and each patch of the integration element is “good” in shape and size for standard Gaussian quadrature. Therefore, all kinds of nearly singular boundary integrals on elements of any shape and size with arbitrary source point location related to the element can be evaluated accurately and efficiently.

Numerical examples for planar and slender elements with various relative location of the source point are presented. The results demonstrate that our method has much better accuracy, efficiency and stability than conventional methods.

The purpose of this paper is to evaluate some numerical integration strategies used in generalized (G)/extended finite element method (XFEM) to solve linear elastic fracture mechanics problems. A range of parameters are here analyzed, evidencing how the numerical integration error and the computational efficiency are improved when particularities from these examples are properly considered.

Numerical integration strategies were implemented in an existing computational environment that provides a finite element method and G/XFEM tools. The main parameters of the analysis are considered and the performance using such strategies is compared with standard integration results.

Known numerical integration strategies suitable for fracture mechanics analysis are studied and implemented. Results from different crack configurations are presented and discussed, highlighting the necessity of alternative integration techniques for problems with singularities and/or discontinuities.

This study presents a variety of fracture mechanics examples solved by G/XFEM in which the use of standard numerical integration with Gauss quadratures results in loss of precision. It is discussed the behaviour of subdivision of elements and mapping of integration points strategies for a range of meshes and cracks geometries, also featuring distorted elements and how they affect strain energy and stress intensity factors evaluation for both strategies.

That part of human behaviour which is not rigidly determined by external constraints can be considered as a sequence of more or less free choices. One can talk of a choice only if it is one of several alternatives, and of a free choice only in so far as it is not determined by conditions over which the individuals have no control. Moreover, we recognise an alternative only if it is actually elected by at least a fraction of a population. This leads to the concept of statistical freedom. Postulates are formulated which must be satisfied by any numerical measures of statistical freedom, and certain mathematical expressions are proposed which are shown to conform to these postulates. Statistical freedom has two fundamental features, which appear as factors in its numerical measure: diversity and independence. The measures of diversity and independence are derived in the first place front a certain model of society, but once they are obtained, the model is discarded, and the statistical coefficients are justified by their mathematical properties. Safeguards against arbitrary manipulation of statistical material are discussed, and the potential use of the new measures is illustrated by application to the problem of choice of profession.

In this paper, a superconvergent patch recovery method is proposed for superconvergent solutions of modes in the finite element post-processing stage of variable geometrical Timoshenko beams. The proposed superconvergent patch recovery method improves the solution speed and accuracy of the finite element analysis of a curved beam. The free vibration and natural frequency of the beam were considered for studying forced vibrations and structural resonance. Beam vibration mode analysis was performed for high-precision vibration mode solutions and frequency values. The proposed method can be used to compute beam vibration modes of beams with different shapes and boundary conditions as well as variable cross sections and curvatures. The purpose of this paper is to address these issues.

An adaptive method was proposed to analyse the in-plane and out-of-plane free vibrations of the variable geometrical Timoshenko beams. In the post-processing stage of the displacement-based finite element method, the superconvergent patch recovery method and high-order shape function interpolation technique were used to obtain the superconvergent solution of mode (displacement). The superconvergent solution of mode was used to estimate the error of the finite element solution of mode in the energy form under the current mesh. Furthermore, an adaptive mesh refinement was proposed by mesh subdivision to derive an optimised mesh and accurate finite element solution to meet the preset error tolerance.

The results computed using the proposed algorithm were in good agreement with those computed using other high-precision algorithms, thus validating the accuracy of the proposed algorithm for beam analysis. The numerical analysis of parabolic curved beams, beams with variable cross sections and curvatures, elliptically curved beams and circularly curved beams helped verify that the solutions of frequencies were consistent with the results obtained using other specially developed methods. The proposed method is well suited for the mesh refinement analysis of a curved beam structure for analysing the changes in high-order vibration mode. The parts where the vibration mode changed significantly were locally densified; a relatively fine mesh division was adopted that validated the reliability of the mesh optimisation processing of the proposed algorithm.

The proposed algorithm can obtain high-precision vibration solutions of variable geometrical Timoshenko beams based on more optimized and reasonable meshes than the conventional finite element method. Furthermore, it can be used for vibration problems of parabolic curved beams, beams with variable cross sections and curvatures, elliptically curved beams and circularly curved beams. The proposed algorithm can be extended for application in superconvergent computation and adaptive analysis of finite element solutions of general structures and solid deformation fields and used for adaptive analysis of more complex plates, shells and three-dimensional structures. Additionally, this method can analyse the vibration and stability of curved members with crack damage to obtain high-precision vibration modes and instability modes under damage defects.

Moderately thick circular cylindrical shells are widely used as supporting structures or storage cavities in structural engineering, rock engineering, and aerospace engineering. In practical engineering, shells often work with micro-cracks or defects. The existence of micro-crack damage may result in the disturbance of dynamic behaviours and even induce accidental dynamic disasters. The free vibration frequency and mode are important parameters for the dynamic performance and damage identification analysis. In particular, stiffness weakening of the local damage region leads to significant changes in the vibration mode, which makes it difficult for the mesh generated in the conventional finite element method to capture a high-precision solution of the local oscillation.

In response to the above problems, this study developed an adaptive finite element method and a crack damage characterisation method for moderately thick circular cylindrical shells. By introducing the inverse power iteration method, error estimation, and mesh subdivision refinement technique for the analysis of finite element eigenvalue problems, an adaptive computation scheme was constructed for the free vibration problem of moderately thick circular cylindrical shells with circumferential crack damage.

Based on typical numerical examples, the established adaptive finite element solution for the free vibration of moderately thick circular cylindrical shells demonstrated its suitability for solving the high-precision free vibration frequency and mode of cylindrical shell structures. The any order frequency and mode shape of cracked cylindrical shells under the conditions of different ring wave numbers, crack locations, crack depths, and multiple cracks were successfully solved. The influences of the location, depth, and number of cracks on the disturbance of dynamic behaviours were analysed.

This study can be used as a reference for the adaptive finite element solution of free vibration of moderately thick circular cylindrical shells with cracks and lays the foundation for further development of a high-performance computation method suitable for the dynamic disturbance and damage identification analysis of general cracked structures.