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Poor bending response is a major shortcoming of lower-order elements due to excessive representation of shear stress/strain field. Advanced finite element (FE) formulations for classical elasticity enhance the bending response by either nullifying or filtering some of the symmetric shear stress/strain modes. Nevertheless, the stress/strain field in Cosserat elasticity is asymmetric; consequently any attempt to nullify or filter the anti-symmetric shear stress/strain modes may lead to failure in the constant couple-stress patch test where the anti-symmetric shear stress/strain field is linear. This paper aims at enhancing the bending response of lower-order elements for Cosserat elasticity problems.

A four-node quadrilateral and an eight-node hexahedron are formulated by hybrid-stress approach. The symmetric stress is assumed as those of Pian and Sumihara and Pian and Tong. The anti-symmetric stress components are first assumed to be completely linear in order to pass the constant couple-stress patch test. The linear modes are then constrained with respect to the prescribed body-couple via the equilibrium conditions.

Numerical tests show that the hybrid elements can strictly pass the constant couple-stress patch test and are markedly more accurate than the conventional elements as well as the incompatible elements for bending problems in Cosserat elasticity.

This paper proposes a hybrid FE formulation to improve the bending response of four-node quadrilateral and eight-node hexahedral elements for Cosserat elasticity problems without compromising the constant couple-stress patch test.

An analytical investigation has been carried out for a simply supported rectangular plate with two different loading conditions by using 3D state space approach (SSA). Also, the accurate location of the neutral plane (N.P.) through the thickness of the plate can be identified: the N.P. is shifted away from the middle plane according to the loading condition. The paper aims to discuss these issues.

SSA and finite element method are used for the determination of structural behaviour of simply supported orthotropic composite plates under different types of loading. The numerical results from a finite element model developed in ABAQUS.

The effect of the plate thickness on displacements and stresses is described quantitatively. It is found that the N.P. of the plate, identified according to the values of the in-plane stresses through the thickness direction, is shifted away from the middle plane. Further investigation shows that the position of the N.P. is loading dependant.

This paper describe the effect of the plate thickness on displacements and stresses quantitatively by using an exact solution called SSA. Also, it is found that the N.P. of the plate, identified according to the values of the in-plane stresses through the thickness direction, is shifted away from the middle plane. Further investigation shows that the position of the N.P. is loading dependant.

To explore the influence of various factors on the adhesion strength of 3D printing materials and chiffon fabrics, and to develop an original design clothing prototype with an extended functionality that would be compatible with the specifics of the circular design.

Four different chiffon fabrics and four 3D printed materials were chosen as the research subjects to determine the influence of various factors on the adhesion strength and ductility. The uniaxial tensile test was used to determine pull-out force and the pull-out elongation from the interlayer.

3D printed TPU elements can be used to join clothing parts made from low-elasticity chiffon fabrics to improve wearing comfort. In order to comply with the circular economy concept, it is important to select such adhesion parameters of the 3D printed elements and the material system that would ensure wear comfort and withstand wear-level loads; and at the end of the life cycle of a garment, the 3D printed elements could be separated from the product and recycled.

The systems developed can be used to renew and repair products, adding originality, individual touch or additional decorative features, while extending the functional possibilities of clothing items in accordance with circular design principles.

Domain integrals, known as volume potentials in 3D elasticity problems, exist in many boundary-type methods, such as the boundary element method (BEM) for inhomogeneous partial differential equations. The purpose of this paper is to develop an accurate and reliable technique to effectively evaluate the volume potentials in 3D elasticity problems.

An adaptive background cell-based domain integration method is proposed for treatment of volume potentials in 3D elasticity problems. The background cells are constructed from the information of the boundary elements based on an oct-tree structure, and the domain integrals are evaluated over the cells rather than volume elements. The cells that contain the boundary elements can be subdivided into smaller sub-cells adaptively according to the sizes and levels of the boundary elements. The fast multipole method (FMM) is further applied in the proposed method to reduce the time complexity of large-scale computation.

The method is a boundary-only discretization method, and it can be applied in the BEM easily. Much computational time is saved by coupling with the FMM. Numerical examples demonstrate the accuracy and efficiency of the proposed method..

Boundary elements are used to create adaptive background cells, and domain integrals are evaluated over the cells rather than volume elements. Large-scale computation is made possible by coupling with the FMM.

A two‐grid iterative method for 3D linear elasticity problems, discretized using quadratic tetrahedral elements is proposed. The conjugate‐gradient method is used as smoother. As compared to the conjugate‐gradient alone, it is shown, via numerical examples, that the method is much more efficient on the basis of computing time and memory allocation. The convergence property of the method is sensitive to the regularity of the problem.

In plane elasticity, a general expression for a mutual work difference integral (MWDI) derived from two stress fields is introduced. Once two physical stress fields are known beforehand, the relevant MWDI can be evaluated exactly from the coefficients in the complex potentials. A biaxial tension model for evaluating defect energy is introduced. A particular MWDI from two fields, one is for the damaged medium under remote biaxial tension and other is for an infinite perfect plate under the same remote biaxial tension, can be defined as a suitable measure of stiffness for the damaged medium, which is called the defect energy ( E (a) ). The suggested model can deal with the cracks, holes, and elastic inclusions in a unique way. The model can also evaluate the defect energies for different damages exactly without dependence on the orientation of damages. Physically, the higher is the defect energy achieved, the more are the involved damages in the medium. The defect energy may be negative, which means a more rigid inclusion is included in the medium. For 3D‐elasticity, a triaxial tension model is introduced for evaluating the defect energy for the damaged medium. For some particular cases, for example, the dissimilar elastic spherical inclusion, or the elliptic flat crack, the relevant defect energies are evaluated.

To describe the mathematics, mechanics and computer code that are involved in deriving the mechanical properties of a 3D composite material with a complicated internal architecture. To inform the reader how an application programming interface (API) can be used with a commercial FEA code to undertake the task. Finally to validate the process an demonstrate the versatility of the process.

The complex architecture of the composite is imported to an FEA environment and meshed. The special code is written in Pascal that applies six sets of constraints to simulate unit strain vectors on a cell of the composite. After six separate analyses are undertaken, the forces necessary to achieve the boundary constraints are summed to provide stresses and hence the necessary coefficients in the stress to strain relationship for the composite. After global FEA the strains in the homogenized material are used as input to the inverse homogenizer so that stress and strain levels in the individual ingredients of the composite can be calculated for the purposes of assessing failure.

The process of writing separate code to operate in conjunction with a commercial FEA code was found to be very reliable, time‐effective and can be of great benefit to engineers researching with composites.

At this state all the materials can only be stressed within their elastic limit. There is no logical impediment to extending the algorithm to increase stresses into the non‐linear range.

The use of the API environment allows third parties to develop application‐specific code that overcomes the increasing generality of commercial FEA codes. The author can easily make the research available to the whole engineering and materials community without losing any intellectual property.

The practical results of this research are now freely available to the whole community and the work demonstrates in a general way how researchers can make their work available without having to write any FEA code, only the things they have researched.

This study highlights the demand for low-cost and high accuracy products through the design and development of new 3D printing technologies. Besides, significant progress has been made in this field. A comparative study helps to understand the latest development in materials and future prospect of this technology.

Nevertheless, a large amount of progress still remains to be made. While some of the works have focused on the performances of the materials, the rest have focused on the development of new methods and techniques in additive manufacturing.

This paper critically evaluates the current 3D printing technologies, including the development and optimizations made to the printing methods, as well as the printed objects. Meanwhile, previous developments in this area and contributions to the modern trend in manufacturing technology are summarized briefly.

The paper can be summarized in three sections. Firstly, the existing printing methods along with the frequently used printing materials, as well as the processing parameters, and the factors which influence the quality and mechanical performances of the printed objects are discussed. Secondly, the optimization techniques, such as topology, shape, structure and mechanical property, are described. Thirdly, the latest development and applications of additive manufacturing are depicted, and the scope of future research in the relevant area is put forward.

This paper gives a bibliographical review of the finite element and boundary element parallel processing techniques from the theoretical and application points of view. Topics include: theory – domain decomposition/partitioning, load balancing, parallel solvers/algorithms, parallel mesh generation, adaptive methods, and visualization/graphics; applications – structural mechanics problems, dynamic problems, material/geometrical non‐linear problems, contact problems, fracture mechanics, field problems, coupled problems, sensitivity and optimization, and other problems; hardware and software environments – hardware environments, programming techniques, and software development and presentations. The bibliography at the end of this paper contains 850 references to papers, conference proceedings and theses/dissertations dealing with presented subjects that were published between 1996 and 2002.

The authors examined the numerical natural frequency analysis of a 2D functionally graded (FG) truncated thick hollow cone using 3D elasticity theory.

The material properties of the 2D-FGM (two dimensional-functionally graded materials) cone are graded along the radial and axial axes of the cone using a power–law distribution. The eigenvalue problem was solved using finite element analysis (FEA) employing graded hexahedral elements, and the verification of the finite element approach was assessed by comparing the current solution to earlier experimental studies.

The effects of semivertex angle, material distribution and the cone configuration on the natural frequencies have been analyzed. For various semivertex angles, thickness, length and power law exponents, many results in the form of natural frequencies and mode shapes are presented for the 2D-FGM cone. As a result, the effects of the given parameters were addressed, and the results were compared, demonstrating the direct efficiency of raising the power–law exponents and cone thickness on the rise of natural frequencies.

For the first time, the numerical natural frequency analysis of a 2D-FG truncated thick hollow truncated cone based on 3D equations of elasticity has been investigated. The material properties of the truncated cone have been distributed along two directions, which has not been considered before in any research for the truncated thick cone. The reason for using these innovative volume fraction functions is the lack of accurate coverage by functions that are available in the literature (Asemi et al., 2011; Babaei et al. 2021).