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Among different types of engineering structures, plates play a significant role. Their analysis necessitates numerical modeling with finite elements, such as triangular, quadrangular or sector plate elements, owing to the intricate geometrical shapes and applied loads. The scope of this study is the development of a new rectangular finite element for thin plate bending based on the strain approach using Airy's function. It is called a rectangular plate finite element using Airy function (RPFEUAF) and has four nodes. Each node had three degrees of freedom: one transverse displacement (w) and two normal rotations (x, y).

Equilibrium conditions are used to generate the interpolation functions for the fields of strain, displacements and stresses. The evolution of the Airy function solutions yielded the selection of these polynomial bi-harmonic functions. The variational principle and the analytical integration approach are used to evaluate the basic stiffness matrix.

The numerical findings for thin plates quickly approach the Kirchhoff solution. The results obtained are compared to the analytical solution based on Kirchhoff theory.

The efficiency of the strain based approach using Airy's function is confirmed, and the robustness of the presented element RPFEUAF is demonstrated. Because of this, the current element is more reliable, better suited for computations and especially intriguing for modeling this kind of structure.

This study implements the fourth-order phase field method (PFM) for modeling fracture in brittle materials. The weak form of the fourth-order PFM requires C¹ basis functions for the crack evolution scalar field in a finite element framework. To address this, non-Sibsonian type shape functions that are nonpolynomial types based on distance measures, are used in the context of natural neighbor shape functions. The capability and efficiency of this method are studied for modeling cracks.

The weak form of the fourth-order PFM is derived from two governing equations for finite element modeling. C⁰ non-Sibsonian shape functions are derived using distance measures on a generalized quad element. Then these shape functions are degree elevated with Bernstein-Bezier (BB) patch to get higher-order continuity (C¹) in the shape function. The quad element is divided into several background triangular elements to apply the Gauss-quadrature rule for numerical integration. Both fourth-order and second-order PFMs are implemented in a finite element framework. The efficiency of the interpolation function is studied in terms of convergence and accuracy for capturing crack topology in the fourth-order PFM.

It is observed that fourth-order PFM has higher accuracy and convergence than second-order PFM using non-Sibsonian type interpolants. The former predicts higher failure loads and failure displacements compared to the second-order model due to the addition of higher-order terms in the energy equation. The fracture pattern is realistic when only the tensile part of the strain energy is taken for fracture evolution. The fracture pattern is also observed in the compressive region when both tensile and compressive energy for crack evolution are taken into account, which is unrealistic. Length scale has a certain specific effect on the failure load of the specimen.

Fourth-order PFM is implemented using C¹ non-Sibsonian type of shape functions. The derivation and implementation are carried out for both the second-order and fourth-order PFM. The length scale effect on both models is shown. The better accuracy and convergence rate of the fourth-order PFM over second-order PFM are studied using the current approach. The critical difference between the isotropic phase field and the hybrid phase field approach is also presented to showcase the importance of strain energy decomposition in PFM.

The purpose of this study is to increasing the gauge factor, reducing the hysteresis error and improving the stability over cyclic deformations of a conductive polylactic acid (CPLA)-based 3D-printed strain sensor by modifying the sensing element geometry.

Five different configurations, namely, linear, serpentine, square, triangular and trapezoidal, of CPLA sensing elements are printed on the thermoplastic polyurethane substrate material individually. The resistance change ratio of the printed sensors, when loaded to a predefined percentage of the maximum strain values over multiple cycles, is recorded. Finally, the thickness of substrate and CPLA and the included angle of the triangular strain sensor are evaluated for their influences on the sensitivity.

The triangular configuration yields the least hysteresis error with high accuracy over repeated loading conditions, because of its uniform stress distribution, whereas the conventional linear configuration produces the maximum sensitivity with low accuracy. The thickness of the substrate and sensing element has more influence over the included angle, in enhancing the sensitivity of the triangular configuration. The sensitivity of the triangular configuration exceeds the linear configuration when printed at ideal sensor dimensional values.

The 3D printing parameters are kept constant for all the configurations; rather it can be varied for improving the performance of the sensor. Furthermore, the influences of stretching rate and nozzle temperature of the sensing material are not considered in this work.

The sensitivity and accuracy of CPLA-based strain sensor are evaluated for modification in its geometry, and the performance metrics are enhanced using the regression modelling.

The objective of the study is to examine the response of reinforced concrete (RC) structures subjected to Near-Fault Ground Motions (NFGM) and highlight the importance of considering various factors including the influence of the relative geographical position of near-fault sites that can affect the structural response during an earthquake.

In this paper, the response of a four-storey RC building subjected to NFGMs with varied characteristics like hanging wall and footwall in conjunction with directivity and the effect of pulse-like ground motions with rupture direction are investigated to understand the combined influence of these factors on the behavior of the structure. Furthermore, the capacity and demand of the structural element are investigated for computing the performance ratio.

Results from this study indicate that the most unfavorable combinations for structural damage due to near-fault ground motion are the hanging wall with forward rupture, the fault normal component of ground motions, and pulse-like ground motions with forward directivity.

The results from this study provide valuable insight into the response of RC structures subjected to NFGM and highlight the importance of considering various factors that can affect the structural response during an earthquake. Moreover, the computation of capacity and demand of the critical beam indicates exceedance of desired limits, resulting in the early deterioration of the structural elements. Finally, the analytical analysis from the present study confirms that the hanging wall with forward ruptures, pulse-like motions, and fling steps are the most unfavorable combinations for seismic structural damage.

This article aims to present a direct solution to handle linear constraints in finite element (FE) analysis without penalties or the Lagrange multipliers introduced.

First, the system of linear equations corresponding to the linear constraints is solved for the leading variables in terms of the free variables and the constants. Then, the reduced system of equilibrium equations with respect to the free variables is derived from the finite-dimensional virtual work equation. Finally, the algorithm is designed.

The proposed procedure is promising in three typical cases: (1) to enforce displacement constraints in any direction; (2) to implement local refinements by allowing hanging nodes from element subdivision and (3) to treat non-matching grids of distinct parts of the problem domain. The procedure is general and suitable for 3D non-linear analyses.

The algorithm is fitted only to the Galerkin-based numerical methods.

The proposed procedure does not need Lagrange multipliers or penalties. The tangential stiffness matrix of the reduced system of equilibrium equations reserves positive definiteness and symmetry. Besides, many contemporary Galerkin-based numerical methods need to tackle the enforcement of the essential conditions, whose weak forms reduce to linear constraints. As a result, the proposed procedure is quite promising.

This study aims to comprehensively investigate the mixed-mode fracture behavior and mechanical properties of selective laser sintering (SLS) polyamide 12 (PA12) components, considering different build orientations and layer thicknesses. The primary objectives include the following. Conducting mixed-mode fracture and mechanical analyses on SLS PA12 parts. Investigating the influence of build orientation and layer thickness on the mechanical properties of SLS-printed components. Examining the fracture mechanisms of SLS-produced Arcan fracture and tensile specimens through experimental methods and finite element analyses.

The research used a combination of experimental techniques and numerical analyses. Tensile and Arcan fracture specimens were fabricated using the SLS process with varying build orientations (X, X–Y, Z) and layer thicknesses (0.1 mm, 0.2 mm). Mechanical properties, including tensile strength, modulus of elasticity and critical stress intensity factor, were quantified through experimental testing. Mixed-mode fracture tests were conducted using a specialized fixture, and finite element analyses using the J-integral method were performed to calculate fracture toughness. Scanning electron microscopy (SEM) was used for detailed morphological analysis of fractured surfaces.

The investigation revealed that the highest tensile properties were achieved in samples fabricated horizontally in the X orientation with a layer thickness of 0.1 mm. Additionally, parts manufactured with a layer thickness of 0.2 mm exhibited favorable mixed-mode fracture behavior. The results emphasize the significance of build orientation and layer thickness in influencing mechanical properties and fracture behavior. SEM analysis provided valuable insights into the failure mechanisms of SLS-produced PA12 components.

This study contributes to the field of additive manufacturing by providing a comprehensive analysis of the mixed-mode fracture behavior and mechanical properties of SLS-produced PA12 components. The investigation offers novel insights into the influence of build orientation and layer thickness on the performance of such components. The combination of experimental testing, numerical analyses and SEM morphological observations enhances the understanding of fracture behavior in additive manufacturing processes. The findings contribute to optimizing the design and manufacturing of high-quality PA12 components using SLS technology.

This paper aims to examine the static compression characteristics of cell topologies in body-centered cubic with vertical struts (BCCZ) and face-centered cubic with vertical struts (FCCZ) along with novel BCCZZ and FCCZZ lattice structures.

The newly developed structures were obtained by adding extra interior vertical struts into the BCCZ and FCCZ configurations. The samples, composed of the AlSi10Mg alloy, were fabricated using the selective laser melting (SLM) additive manufacturing technique. The specific compressive strength and failure behavior of the manufactured lattice structures were investigated, and comparative analysis among them was done.

The results revealed that the specific strength of BCCZZ and FCCZZ samples with 0.5 mm strut diameter exhibited approximately a 23% and 18% increase, respectively, compared with the BCCZ and FCCZ samples with identical strut diameters. Moreover, finite element analysis was carried out to simulate the compressive response of the lattice structures, which could be used to predict their strength and collapse mode. The findings showed that while the local buckling of lattice cells is the major failure mode, the samples subsequently collapsed along a diagonal shear band.

An original and systematic investigation was conducted to explore the compression properties of newly fabricated lattice structures using SLM. The results revealed that the novel FCCZZ and BCCZZ structures were found to possess significant potential for load-bearing applications.

The purpose of this study is to use the corrected stress field theory to derive the shear capacity of geopolymer concrete beams (GPC) and consider the shear-span ratio as a major factor affecting the shear capacity. This research aims to provide guidance for studying the shear capacity of GPC and to observe how the failure modes of beams change with the variation of the shear-span ratio, thereby discovering underlying patterns.

Three test beams with shear span ratios of 1.5, 2.0 and 2.5 are investigated in this paper. For GPC beams with shear-span ratios of 1.5, 2.0 and 2.5, ultimate capacities are 337kN, 235kN and 195kN, respectively. Transitioning from 1.5 to 2.0 results in a 30% decrease in capacity, a reduction of 102kN. Moving from 2.0 to 2.5 sees a 17% decrease, with a loss of 40KN in capacity. A shear capacity formula, derived from modified compression field theory and considering concrete shear strength, stirrups and aggregate interlocking force, was validated through finite element modeling. Additionally, models with shear ratios of 1 and 3 were created to observe crack propagation patterns.

For GPC beams with shear-span ratios of 1.5, 2.0 and 2.5, ultimate capacities of 337KN, 235KN and 195KN are achieved, respectively. A reduction in capacity of 102KN occurs when transitioning from 1.5 to 2.0 and a decrease of 40KN is observed when moving from 2.0 to 2.5. The average test-to-theory ratio, at 1.015 with a variance of 0.001, demonstrates strong agreement. ABAQUS models beams with ratios ranging from 1.0 to 3.0, revealing crack trends indicative of reduced crack angles with higher ratios. The failure mode observed in the models aligns with experimental results.

This article provides a reference for the shear bearing capacity formula of geopolymer reinforced concrete (GRC) beams, addressing the limited research in this area. Additionally, an exponential model incorporating the shear-span ratio as a variable was employed to calculate the shear capacity, based on previous studies. Moreover, the analysis of shear capacity results integrated literature from prior research. By fitting previous experimental data to the proposed formula, the accuracy of this study's derived formula was further validated, with theoretical values aligning well with experimental results. Additionally, guidance is offered for utilizing ABAQUS in simulating the failure process of GRC beams.

The calculation and design of the structures are carried out with the aim of obtaining a sufficiently ductile behavior to allow the structure to undergo displacements, without risk of sudden breaks or loss of stability. The purpose of this study is to develop and validate a computer program (Thin beam2), allowing the modeling and simulation of the nonlinear behavior of reinforced concrete elements, on the other part, it is estimating the local and global ductility of the sections or elements constituting these structures.

The authors present two nonlinear analysis methods to carry out a parametric study of the factors influencing the local and global ductility of reinforced concrete structures. The first consists in evaluating the nonlinear behavior at the level of the cross-section of the reinforced concrete elements used in the elaborate Sectenol 1 program, it allows us to have the local ductility. The second, allows us to evaluate the nonlinear behavior of the element used in the modified thin beam 2 program, it allows us to estimate the overall ductility of the element.

The validation results of the Thin beam2 program are very satisfactory, by conferring the analytic and experimental results obtained by various researchers and the parametric study shows that each factor such as the compressive strength of the concrete has a favorable effect on ductility. Conversely, the normal compression force and the high resistance of tensioned reinforcements adversely affect ductility.

The reliability of the two programs lies in obtaining the local and global ductility of reinforced concrete structures because the calculation and design of the structures are carried out with the aim of obtaining ductile behavior without risk of breakage and instability.

The purpose of this study is to develop an efficient numerical procedure for simulating the effect of printing orientation, as one of the primary sources of anisotropy in 3D-printed components, on their fracture properties.

The extended finite element method and the cohesive zone model (XFEM-CZM) are used to develop subroutines for fracture simulation. The ability of two prevalent models, i.e. the continuous-varying fracture properties (CVF) model and the weak plane model (WPM), and a combination of both models (WPM-CVF) are evaluated to capture fracture behavior of the additively manufactured samples. These models are based on the non-local and local forms of the anisotropic maximum tangential stress criterion. The numerical models are assessed by comparing their results with experimental outcomes of 16 different configurations of polycarbonate samples printed using the material extrusion technique.

The results demonstrate that the CVF exaggerates the level of anisotropy, and the WPM cannot detect the mild anisotropy of 3D-printed parts, while the WPM-CVF produces the best results. Additionally, the non-local scheme outperforms the local approach in terms of finite element analysis performance, such as mesh dependency, robustness, etc.

This paper provides a method for modeling anisotropic fracture in 3D-printed objects. A new damage model based on a combination of two prevalent models is offered. Moreover, the developed subroutines for implementing the non-local anisotropic fracture criterion enable a reliable crack propagation simulation in media with varying degrees of complication, such as anisotropy.