This article presents a novel methodology for the simultaneous optimization of both structural topology and printing path in 3D concrete printing (3DCP), addressing a critical gap between digital design and physical manufacturability. Unlike conventional sequential approaches, our framework is grounded in discrete frame structures, which inherently reflect the filament-based nature of 3DCP, thereby enhancing geometric and mechanical fidelity. The proposed formulation strategically leverages the inherent anisotropy of printed concrete by aligning the printing direction along the longitudinal axis of each frame member to maximize strength and material efficiency. Key manufacturing constraints are integrated directly into the optimization process: member widths are restricted to integer multiples of the nozzle size, and the printing path is enforced as a globally continuous, non-intersecting, and non-overlapping Eulerian circuit through a mixed-integer linear programming model. The efficacy of this simultaneous optimization approach is demonstrated through a series of benchmark problems, which confirm that the resulting designs not only satisfy strict structural displacement and stress constraints with minimal material usage but are also readily manufacturable via direct "one-stroke" printing. This work establishes a foundational integration of structural performance and manufacturability, paving the way for more efficient and reliable 3DCP applications.

To overcome the strong mesh dependence and low computational efficiency of conventional phase-field fracture simulations based on finite element method (FEM), this study proposes a novel framework for efficient and accurate fracture analysis by integrating the Quadrature Element Method (QEM) into the phase-field formulation. In this formulation, the variational functional is discretized via numerical integration, and spatial derivatives are subsequently approximated using differential quadrature at integration points, enabling high-order approximation without explicitly constructing conventional FEM element shape functions for field interpolation; the differential-quadrature weighting coefficients are instead derived from Lagrange cardinal interpolation polynomials. This technology facilitates flexible high-order element construction and accurate representation of stress fields near crack tips. In addition, an alternate minimization algorithm is employed to solve the coupling between displacement and phase-field evolution while maintaining the crack irreversibility. The performance of the proposed method is demonstrated through a series of benchmark problems, including three-point bending, single-edge shear, asymmetric double-notched tension, and a 3D-printed Y-shaped cracking specimen. Numerical comparisons show approximately 95.6% fewer degrees of freedom in the single-edge shear specimen and up to 99.98% fewer elements in the asymmetric double-notched tensile specimen than in the cited FEM-based phase-field models, demonstrating substantial reductions in discretized model size. Moreover, the proposed method provides accurate near-tip stress predictions on coarse meshes, mitigates locking, and maintains stable numerical behavior for the mildly distorted mesh examined. Overall, the combination of high-order approximation and coarse-mesh adaptability makes the proposed phase-field QEM a promising solution for simulating complex crack evolution in engineering applications.

A novel methodology is introduced for simultaneously optimizing both the structural topology and printing paths in 3D concrete printing (3DCP). Drawing inspiration from the inherent geometric characteristics of 3DCP, this approach anchors its optimization framework within discrete frame structures. Beyond conventional frame topology optimization, we introduced the concept of simultaneous path optimization, bridging the gap between optimal design conception and its seamless realization in manufacturing. Leveraging the mechanical anisotropy inherent to 3DCP, we strategically orient the printing directions such that each frame member is printed along its longitudinal axis, optimizing for strength and material efficiency. To ensure direct printability, we impose constraints whereby the width of each member must be an integer multiple of the nozzle size, and the printing path must traverse continuously, covering the entire design without any intersections or overlaps. An Eulerian circuit, rooted in graph theory, fulfills part of these requirements, with additional constraints introduced to rigorously eliminate intersections and overlaps. The comprehensive simultaneous optimization problem is then formulated as a Mixed-Integer Linear Program (MILP), which is readily solvable. The application of this methodology to various test problems has yielded successful outcomes, demonstrating the efficacy and practicality of our approach in achieving simultaneous optimization of both structural topology and printing paths in 3DCP.

A methodology for determining elastic engineering constants in an orthotropic constitutive model of hardened three-dimensional (3D)-printed concrete (3DPC) is introduced in this paper. The 3DPC material's unique configuration of filaments and layers weakens the mechanical interfaces between them, resulting in clear anisotropy along the three principal directions. To address this, a numerical model of a composite representative volume element (RVE) is created that combines a continuum concrete damaged plasticity model for the filaments with an interfacial cohesive zone model for the interfaces. The model's parameter values are determined through uniaxial compression, splitting tension, cross-bonded tension, and inclined shear tests. By exploring the model's design space using the design of experiments (DOE) technique, quantitative relationships between the orthotropic elastic engineering constants and the material properties of the filaments and interfaces are obtained, leading to explicit and simple formulas. Comparisons between numerical and experimental results for two hollow beams validate the effectiveness of the developed formulas.

This study systematically investigates the bending performance of 3D printed concrete (3DPC) grid components, focusing on the synergistic effects of printing patterns and interfacial anisotropy. Experimental and numerical analyses were conducted on W- and Y-grid specimens fabricated with 10 mm and 20 mm nozzles. A refined finite element model (RFEM) integrating plastic damage elements for filaments and bilinear cohesive zone models (CZM) for interfaces was developed. Key findings reveal that Y-grid components exhibit 80 % higher load-bearing capacity than W-grid counterparts, attributed to enhanced node strength, uniform stress distribution, and increased moment of inertia. Smaller nozzles improve mechanical performance by reducing interfacial defects, with 10 mm nozzles increasing ultimate loads by 10-24 % compared to 20 mm nozzles. Crucially, interfacial damage remained absent prior to structural failure, demonstrating that optimized printing patterns can mitigate anisotropy effects. The validated RFEM achieved less than 10 % error in predicting failure loads and displacements, confirming its utility for 3DPC design. This work advances the understanding of pattern-driven structural optimization in additive manufacturing and provides a computational framework for performance prediction.

In this study, four specimens with two cross-section patterns, the W-shape and Y-shape, are printed by using two nozzle sizes to study the effects of the printed patterns and nozzle size on the mechanics properties of 3D Printed Concrete (3DPC) structures. The four-point loading tests are conducted and the Digital Image Correlation (DIC) analysis technology is used. The results showed that the load capacity of the Y-shaped specimens is about 10

It is well recognized that layer and filament interfaces are the mechanically weakest locations in 3D printed concrete (3DPC) structures. Therefore, interfacial cracking between the layers and filaments is investigated experimentally and numerically. First, direct tensile and inclined shear tests are carried out to measure the tensile and shear load-displacement relationships. Displacement and strain are recorded using the digital image correlation (DIC) technique. Parameter values required in a cohesive zone model (CZM) for simulating the interfacial cracking are extracted from the experimental data. Then a finite element model incorporating the CZM is established to predict the interfacial cracking. The effectiveness of the numerical model is verified by comparing the simulation results with the experimental data.

The relationship between crack comprehensive characteristics and the stiffness of RC beams is investigated through experimental tests and numerical simulations. A synthetic parameter, the surface damage ratio (SDR), is proposed to represent the comprehensive characteristics of cracks, including crack width, length and location. Crack propagation in RC beams is simulated using a dual-damage parameter plastic damage model. A method for calculating the width and length of cracks is developed based on integral point strains and element equivalent length. The accuracy of this method is verified by comparing it with the results of four-point bending tests on RC T-beams and rectangular beams. Correlation analysis indicates that the cracks in different zones have varying impacts on beam stiffness, with crack length in the bending area and crack width in the shear area having a greater impact than others. To consider the comprehensive characteristics of cracks and their impact on beam stiffness, the SDR, the ratio between the entire crack area and the intact area of the beam surface, is proposed. The proposed parameter is shown to increase linearly with load, resulting in beam stiffness degradation following a power law. The accuracy and applicability of the proposed SDR and its correlation with load and stiffness are verified through load tests on rectangular beams with different reinforcement ratios using Cervenka's test. Parameter analysis has shown that the section modulus, concrete strength, reinforcement arrangement, and ratios significantly influence how beam stiffness varies with SDR. The presented simulation model for concrete crack evolution, combined with the synthetic parameter of crack characteristics, and the correlation analysis, provide a valuable approach for the safety evaluation of concrete beams during their service life.

Wave propagation in elastic solids is analyzed by a space-time discontinuous Galerkin quadrature element method. First, the space-time quadrature element is conveniently formulated based on the space-time discontinuous Galerkin formulation. This method treats both the spatial and temporal domains in a unified manner, enabling it to handle not only structured space-time meshes but also unstructured ones. It effectively captures discontinuities or sharp gradients in the solution. To transform the formulation into a system of algebraic equations, the Gauss-Lobatto quadrature rule and the differential quadrature analog are utilized. High-order elements are constructed simply by increasing the order of integration and differentiation without the laborious construction of shape functions. Then, dispersion analysis is conducted for one- and two-dimensional elements. The analysis reveals that as the Courant number decreases, the total dispersion error monotonically converges to the spatial dispersion error, which can be reduced by increasing the element order. Additionally, high-order elements nearly eliminate numerical anisotropy in different directions. Finally, several numerical examples of elastic wave propagation validate the method's effectiveness and high accuracy.

In this paper, J-integral and T*-integral in elastic–plastic fracture are computed by the quadrature element method (QEM). Since high stress gradients exist in the immediate vicinity of the crack front, computing these integrals accurately is not a trivial task. The QEM facilitates the construction of arbitrarily high-order elements, which effectively capture the stress gradients, making it particularly suitable for this computation. After performing an elastoplastic stress–strain analysis of the fracture problem, the stress and deformation states are further formulated to compute the integrals. The integrals are formulated in several forms, including the contour and domain forms, as well as the incremental and total forms. Classical numerical examples are solved to demonstrate the effectiveness and high accuracy of the method. Overall, the equivalent domain integral (EDI) form outperforms the contour integral form because errors at the local contour have less effect on the integral. Moreover, the QEM yields more accurate solutions than the popular finite element method (FEM) that employs low-order finite elements and shares the same number of degrees of freedom. Additionally, it is found that the EDI form solution is not very sensitive to the specific type of the S function. Therefore, a linear function is suggested for convenience.

Three time-discontinuous Galerkin quadrature element methods (TDGQEMs) are developed for structural dynamic problems. The weak-form time-discontinuous Galerkin (TDG) statements, which are capable of capturing possible displacement and/or velocity discontinuities, are employed to formulate the three types of quadrature elements, i.e., single -field, single- field/least-squares and two-field. Gauss-Lobatto quadrature rule and the differential quadrature analog are used to turn the weak- form TDG statements into a system of algebraic equations. The stability, accuracy and numerical dissipation and dispersion properties of the formulated elements are examined. It is found that all the elements are unconditionally stable, the order of accuracy is equal to two times the element order minus one or two times the element order, and the high -order elements possess desired high numerical dissipation in the high-frequency domain and low numerical dissipation and dispersion in the low- frequency domain. Three fundamental numerical examples are investigated to demonstrate the effectiveness and high accuracy of the elements, as compared with the commonly used time integration schemes.

A modified deflection theory is developed for preliminary design of self-anchored suspension bridges. The proposed theory modifies the questionable approach of the existing theory considering the initial fabrication camber and overcomes the limitation that the hangers are assumed inextensible, which results in a stiffer bridge system and thus underestimation of the main cable and girder deflections. In addition, in order to avoid the inconvenience of solving a system of nonlinear equations iteratively for the preliminary design, the tower flexural stiffness is neglected rationally to obtain a system of linear equations only. With the aid of all force equilibrium and deformation compatibility conditions for the entire bridge system, the modified deflection theory is formulated. Its solution procedure is presented, which leads to a complicated sixth-order variable-coefficient ordinary differential equation, and a practical approximate solution to the equation is sought. To verify the proposed theory, a bridge example is investigated, and the results are compared to those from the previous deflection theory and complex finite element analysis. The comparisons demonstrate the effectiveness of the modified deflection theory.

A novel quadrature element for performing plane stress elastoplastic analysis is introduced in this paper. Differing from the popular finite-element method, the quadrature-element method (QEM) first evaluates the integration in the weak-form statement of the problem by an integral quadrature scheme, and then approximates the differentiation at the discrete integration points by the differential quadrature analog. As a result, the QEM avoids construction of shape functions and obtains higher-order elements easily by just increasing the order of integration. The usage of higher-order elements leads to more accurate solutions and coarser geometric meshes without detriment to the computational scale because the number of degrees of freedom is maintained. In addition, the element nodes in the QEM are the same as the integration points that possess physical meanings such as strains and stresses, which is crucial in the elastoplastic analysis for determining the elastic/plastic state of the nodes. A straightforward elastoplastic quadrature-element formulation is developed. Incremental-iterative and return mapping solution schemes are adopted to implement the quadrature element for the elastoplastic analysis. Numerical examples are presented to demonstrate the effectiveness and high accuracy of the proposed approach.

The phase field method (PFM) provides a novel perspective for fracture computation. It is capable of simulating the whole process of crack propagation without introducing additional fracture criteria and complex crack path-tracking techniques. From the computational point of view, however, the PFM requires very fine meshes for the conventional numerical methods to accurately characterize the crack, which leads to huge computational costs. This paper employs the quadrature element method (QEM) to compute the phase field model for the brittle fracture. Through the computation of a benchmark example, the accuracy and low cost of the present method are verified. The QEM, in comparison with the existing methods, can accurately simulate the crack propagation process using a very coarse mesh and thus much fewer degrees of freedom.

As a relatively new computational method, the weak-form quadrature element method (QEM) has attracted more and more worldwide attention recently. However, there exist different formulations, even different names, for the QEM in the literature. To remove possible confusion caused by them, a comparative review is carried out in this paper. The step-by-step procedure of the formulations is examined in detail by a simple one-dimensional bar element, and the nature of each step is revealed carefully. Similarities and differences between the different formulations are summarized after the scrutiny. Based on the full understanding of the QEM, a comprehensive assessment of the method is conducted by comparing several relevant aspects. Superiorities and limitations of the QEM are discussed and its future research directions are pointed out. Finally, a chronological list of research papers related to the QEM since 2017 is presented. State-of-the-art developments and applications of the method are highlighted.

In order to mitigate dynamic responses of floating offshore wind turbines (FOWTs) under combined wind-wave-current loading, employment of structural control techniques is often considered. In this paper, a novel concept of a passive FOWT structure is proposed to overcome the previous limitations on space and mass of tuned mass dampers (TMDs). The conceptual design is examined on the basis of a finite element model. The dynamic responses, mainly roll and pitch rotations, are compared between the controlled and uncontrolled FOWTs. Subsequently, a parametric study is conducted and the main parameters in the model are optimised accordingly. Finally, the optimal performance of the proposed FOWT structure demonstrates the effectiveness of the proposed design, and also its superiority over the existing concepts.

Multiple crack propagation and coalescence in two-dimensional linear elastic media were modeled using the finite-element method (FEM) in conjunction with the subregion generalized variational principle. The proposed approach computes the stress intensity factor (SIF) accurately, as proved in a previous work. The approach results in regular geometric meshes. A multiple crack propagation scheme was developed in this study. The scheme follows the crack propagation by moving just the complementary energy subregion on the basis of the regular mesh. Consequently, it requires only minimal local remeshing without affecting most of the existing mesh. The scheme can handle crack coalescence easily. These advantages simplify the modeling and thus improve the efficiency. Four numerical examples, including a structure containing 10 cracks, were investigated to demonstrate the accuracy and efficiency of the proposed approach.

A novel curved beam quadrature element is presented for geometrically nonlinear analysis of spatial curved beams. Starting from the incremental virtual work equation of the curved beam, the weak form quadrature element method (QEM) is employed to derive the elastic stiffness, geometric stiffness, and induced moment matrices of the curved beam with due account taken of the large rotations in three-dimensional space. All the stiffness matrices are adopted in the incremental-iterative analysis using the generalized displacement control (GDC) method, with specific considerations for the predictor and corrector phases. By testing the constructed curved beam quadrature element with four benchmark problems, it is demonstrated that the element avoids the shear and membrane locking phenomena due to its convenient feature of high-order approximation. In addition, the element is capable of predicting large displacements and rotations, as well as postbuckling paths of spatial beams. Especially, the presented element is featured by unifying the analyses for both curved and straight beams.

An improved approach using the finite element method is proposed for computation of stress intensity factors. The approach is based on a subregion generalized variational principle that divides an entire cracked region into two subregions, a complementary energy subregion around a crack tip and a potential energy subregion for the rest. Finite elements are employed in the potential energy subregion. A rectangular complementary energy subregion, instead of the previous circular one, is constructed for the purpose of a regular mesh. The improved approach is reformulated and validated by four classic numerical examples. Effects of involved parameters on accuracy of the approach are investigated thoroughly. Their optimal values are recommended accordingly.

The accurate computation of stress intensity factors (SIFs) of face-loaded cracks is of significant importance for engineering practices. Based on the analytical stress field of a central crack in an infinite plane subjected to a pair of crack-face concentrated forces, a simple stress substitution approach that replaces the unknown actual stress field by that of the Williams' solution for traction-free cracks is proposed and used in conjunction with the subregion generalized variational principle and quadrature element method (QEM) for computation of the SIF. This approach is validated by a series of representative problems, including different crack configurations and loading conditions. The comparisons between the analytical or approximate solutions and the numerical results suggest that the approach produces reasonably accurate SIFs when the size of the complementary energy subregion is confined to be 0.2-0.3 times the (half) crack length, even with the coarsest mesh. The accuracy can be further improved by smaller subregion size and smaller elemental maximum aspect ratio.