Finite Element Method Analysis Research Articles

Coupled CFD-FEM modeling of fluid–thermal–structural interaction in a single-strand tundish

A mathematical model has been developed to study the fluid–thermal–structural interaction in a single-strand tundish based on a coupled computational fluid dynamics (CFD) and finite element method (FEM) approach. The flow pattern and temperature distribution of the molten steel were predicted by the CFD calculation. Heat transfer and thermal stress profiles in the solid layers were investigated by the FEM analysis. Case studies were carried out comparatively to investigate the effect of tundish preheating and thermal insulation. The results show that tundish preheating can maintain the desired temperature of the molten steel at the exit. The heating efficiency drops significantly after 3 h of preheating. Reducing the thermal conductivity of the insulation material will reduce the temperature of the tundish shell and increase the thermal stress on the working lining. The modeling results can be used to improve the reliability and lifetime of the tundish and reduce production costs.

FEM simulations applied to the failure analysis of RC structure under the influence of municipal sewage pressure

The paper discusses a failure mechanism of reinforced concrete (RC) structure with steel cover that failed under the influence of municipal sewage pressure. To explain the reasons of failure, in-situ measurements, laboratory experiments and comprehensive Finite Element Method (FEM) computations were performed. Non-destructive in-situ scanning tests were carried out to determine quantity and cover thickness of embedded reinforcement bars, simultaneously, laboratory tests regarding concrete and shotcrete thickness, density and compressive strength were performed on samples prepared from core drills taken from the RC structure. FEM computations were carried out with the constitutive continuum model for concrete and steel with material parameters designated on the basis of stress–strain curves in uniaxial compression and uniaxial tension, respectively. An isotropic coupled elasto-plastic-damage formulation based on the strain equivalence hypothesis was used. In order to describe strain localization in concrete, model was enhanced in a softening regime by a characteristic length of micro-structure by means of a non-local theory. FEM analyses were carried out for different values of sewage pressure. The main attention was paid to the evolution of steel cover deformation and strain localization of the RC ceiling slab. FEM results revealed strong dependence between a bond-slip between anchors and steel cover deformation as well as between sewage pressure value and strain localization pattern of RC structure. Mechanism of the structure failure under complex loading conditions was realistically captured and its reasons were discussed in detail.

Optimal error estimates of a non-uniform IMEX-L1 finite element method for time fractional PDEs and PIDEs

Stability and optimal convergence analysis of a non-uniform implicit-explicit L1 finite element method (IMEX-L1-FEM) is studied for a class of time-fractional linear partial differential/integro-differential equations with non-self-adjoint elliptic part having (space-time) variable coefficients. The proposed scheme is based on a combination of an IMEX-L1 method on graded mesh in the temporal direction and a finite element method in the spatial direction. With the help of a discrete fractional Grönwall inequality, global almost optimal error estimates in L2- and H1-norms are derived for the problem with initial data u0∈H01(Ω)∩H2(Ω). The novelty of our approach is based on managing the interaction of the L1 approximation of the fractional derivative and the time discrete elliptic operator to derive the optimal estimate in H1-norm directly. Furthermore, a super convergence result is established when the elliptic operator is self-adjoint with time and space varying coefficients, and as a consequence, an L∞ error estimate is obtained for 2D problems that too with the initial condition is in H01(Ω)∩H2(Ω). All results proved in this paper are valid uniformly as α→1−, where α is the order of the Caputo fractional derivative. Numerical experiments are presented to validate our theoretical findings.

Soft hand with programmable grasping mode for dexterous manipulation

Many soft hands usually preprogram desired motions using oblique actuators, which limits their motion diversity and adaptability. To achieve high compliance and adaptability, this paper proposes a novel soft hand with a hybrid actuator system that can demonstrate both pure bending and helical motions. First, the structure and actuation system of the soft hand are presented. A direct-current motor is used to rotate the actuators. A pump is used to output sufficient torque to bend the soft hand. Second, a theoretical model and Finite Element Analysis (FEA) method are used to analyze the bending performance at various pressures. Then, a control method is proposed to regulate the helical radius of the soft hand in real time by adjusting the rotation angle and pressure simultaneously. Furthermore, experimental results verify the feasibility of programmable and dexterous grasping according to the shape of objects based on the independent control of bending and helical motions.

Experimental and FEA Simulations Using ANSYS on the Mechanical Properties of Laminated Object Manufacturing (LOM) 3D-Printed Woven Jute Fiber-Reinforced PLA Laminates

The mechanical properties of woven jute fiber-reinforced PLA polymer laminates additively manufactured through Laminated Object Manufacturing (LOM) technology are simulated using the finite element method in this work. Woven jute fiber reinforcements are used to strengthen bio-thermoplastic PLA polymers in creating highly biodegradable composite structures that can serve as one of the environmentally friendly alternatives for synthetic composites. A LOM 3D printer prototype was designed and built by the authors. All woven jute/PLA biocomposite laminated specimens made using the built prototype in this study had their tensile and flexural properties measured using ASTM test standards. These laminated structures were modeled using the ANSYS Mechanical Composite PrepPost (ACP) module, and then both testing processes were simulated using the experimentally measured input values. The FEA simulation results indicated a close match with experimental results, with a maximum difference of 9.18%. This study served as an exemplary case study using the FEA method to predict the mechanical behaviors of biocomposite laminate materials made through a novel manufacturing process.

Design of Mixing Device Shafts Based on a Proposed Calculation Method Supported by Finite Element Method Analysis

The elasticity of bearings as well as their clearance have an essential influence on the total arrow and, therefore, on their own pulsation. In most of the literature, this elasticity is neglected in the calculation of shaft deflections. In some work, the elasticity of the bearings has been taken into account when calculating the deflection of the mixing device shaft, but this has been carried out on the basis of a high degree of customization: the behavior of the bearings has been considered linearly elastic, which does not correspond to reality because according to the elastic response of the bearing, it is a nonlinear function of the radial displacement. When the shaft of a mixing device operates in a pressure vessel, at the outlet of the pressure vessel, the shaft is provided with a sealing device, which can be considered a third bearing. This aspect is also not taken into account in the calculation of the shaft’s deflection, which leads to a certain degree of error in its determination. This study aims to highlight the influence of the elasticity of the bearings and the sealing device on the stiffness of the shaft and to propose a method that supports a calculation program for calculating the elastic line of a vertical cantilever shaft, considering the role played by the bearings in the case that they behave nonlinearly and the sealing device as the third bearing. This problem was solved both by applying our own method and with the help of the FEM.

Finite element simulation of treatment with locking plate for distal fibula fractures.

An improved Finite Element Model(FEM) is applied to compare the biomechanical stability of plates with three different options in the treatment of distal fibula fractures in this study. The Computed Tomography(CT) scan of the knee to ankle segment of a volunteer was performed. A 3D fibula FEM was reconstructed based on the CT data. Three different loads (uni-pedal standing, torsion, and twisting) were applied, the same as in the experiments in the literature. The stresses and strains of the three options were compared under the same loads, using a 4-hole locking plate (Option A), a 5-hole locking plate (Option B), and a 6-hole locking plate (Option C) in a standard plate for lateral internal fixation. The simulation results show that all three options showed a stress masking effect. Option C had the best overall biomechanical performance and could effectively distribute the transferred weight. This is because option C has greater torsional stiffness and better biomechanical stability than options A and B, and therefore, option C is the recommended internal fixation method for distal fibula fractures. The Finite Element Analysis(FEA) method developed in this work applies to the stress analysis of fracture treatment options in other body parts.

An adaptive multi-output Gaussian process surrogate model for large-scale parameter estimation problems

PurposeParameter estimation in complex engineering structures typically necessitates repeated calculations using simulation models, leading to significant computational costs. This paper aims to introduce an adaptive multi-output Gaussian process (MOGP) surrogate model for parameter estimation in time-consuming models.Design/methodology/approachThe MOGP surrogate model is established to replace the computationally expensive finite element method (FEM) analysis during the estimation process. We propose a novel adaptive sampling method for MOGP inspired by the traditional expected improvement (EI) method, aiming to reduce the number of required sample points for building the surrogate model. Two mathematical examples and an application in the back analysis of a concrete arch dam are tested to demonstrate the effectiveness of the proposed method.FindingsThe numerical results show that the proposed method requires a relatively small number of sample points to achieve accurate estimates. The proposed adaptive sampling method combined with the MOGP surrogate model shows an obvious advantage in parameter estimation problems involving expensive-to-evaluate models, particularly those with high-dimensional output.Originality/valueA novel adaptive sampling method for establishing the MOGP surrogate model is proposed to accelerate the procedure of solving large-scale parameter estimation problems. This modified adaptive sampling method, based on the traditional EI method, is better suited for multi-output problems, making it highly valuable for numerous practical engineering applications.

The effects of wrinkle distributions on the mechanical characteristics of unidirectional glass fiber-reinforced composites

Wrinkle defects are major manufacturing defects that can reduce the mechanical properties of fiber-reinforced composites, especially their compressive strength. There are differences in the effects of various wrinkle distributions on compression failure. In this work, unidirectional glass fiber-reinforced samples with different thicknesses and wrinkle distributions were manufactured and tested. The corresponding high-fidelity three-dimensional finite element (FE) models are established and combined with a progressive damage analysis method to reveal compression failure behavior. The accuracy of the FE analysis method is verified by combining experimental results. Then, the parameter analyses are conducted to study the effects of wrinkle distributions on the knockdown in compressive mechanical properties, with some corresponding conclusions drawn. The results indicate that the dependence of compressive strength on various wrinkle distributions can be determined.

Controllable manipulation of surface waves via a ferromagnetic elastic metasurface

In this paper, we study the propagation of surface waves on an A-shape metasurface, whose structure of the unit-cell is composed regularly of an A-shape surface column (made of steel), a thin magnetorheological plate and a soft thick rubber base. On the basis of the commercial program COMSOL Multiphysics, finite element method (FEM) analyses are carried out. The localization of elastic waves surrounding the surface allows surface waves to be distinguished among various complex wave modes. By adjusting the geometry, the A-shape surface column can be transformed from snowflake to A-shape. Owing to the C3v symmetry system, a Dirac cone of surface wave is observed in a snowflake metasurface. When the surface column changes to A-shape, the C3v symmetry is broken, making the Dirac cone vanish and a new band gap of surface waves arise. The band gap can be opened or closed by changing a geometric parameter, which determines the shape of the surface column changing from gadarene A-shape to snowflake or even upturned A-shape. Furthermore, we discover that although the topological phases of the gadarene A-shape and upturned A-shape metasurfaces are opposite, they share overlapped band gaps. Based on this phenomenon, we design a topological insulator for surface waves, whose super-cell is composed of gadarene A-shape units and upturned A-shape units. Through the calculation of the super-cell band structure, we observe the topologically protected interface states (TPISs). Subsequently, we design several waveguides whose paths are controllable. Up to now, most of the existing metasurfaces are made of passive materials, whose properties cannot be adjusted in real time, making them inconvenient for engineering applications when external conditions are changed. Therefore, we use tunable magnetorheological elastomer (MRE) to control the properties of the topological insulators. The stiffness of the surface layer can be converted by applying a magnetic field, which makes the topological metasurface controllable. These intelligent topological insulators may find important applications in the design of surface acoustic wave (SAW) devices.

Simplified finite-element analysis method for local and global prediction on axial compression behavior of square spiral-confined reinforced concrete-filled steel tubular columns

Square spiral-confined reinforced concrete-filled steel tubular (SSCRCFST) columns have recently been proposed as an advanced form of composite columns. However, there is still a lack of an efficient approach that can accurately predict both their section-average behavior and local concrete behavior. This paper presented a novel simplified method combining elastic finite element analysis with accurate material laws of concrete, steel tube and longitudinal bar to analyze the axially compressive behavior of SSCRCFST columns. The proposed method utilized elastic finite-element analysis to approximate the distribution and ultimate state of confining stress within each core concrete element, which was then substituted into the Mander confined concrete model to obtain the strength enhancement in each core concrete element subjected to different level of lateral confinement. Finally, the integrated compressive curve of a column can be derived by summarizing the strength of all elements. Verification of the proposed method against a large test database confirmed its capability to accurately capture the results of existing compression tests of SSCRCFST columns. The proposed computationally efficient method was then used to investigate both the section-average and local behavior of SSCRCFST column under monotonic compression for an improved understanding of the confinement mechanism. Finally, a reasonably modified design method for the axial strength of SSCRCFST column was proposed based on research findings in this study, which led to the continuity in the axial strength predictions of SSCRCFST columns with various corner radius ratio and showed good agreement with the test results.

AN APPROACH OF WEB STIFFENER CALCULATION IN THIN-WALLED COLUMNS

This article presents an analytical approach for calculating web stiffeners in thin-walled columns. A novel method is introduced, which treats each bending point in the cross-section web as a separate stiffener. The advantages of this calculation method are discussed, highlighting its increased versatility in designing cross-section geometry. The load-bearing strength of axially compressed thin-walled closed cross-section columns, calculated using this method, is compared to analytical calculations based on the Eurocode 3-1-3 methodology and to the finite element method analysis. Calculation results of columns with cross-sections including shallow web stiffeners were up to 9.22% less conservative when compared to the Eurocode 3-1-3 methodology. The results demonstrate great compliance of the proposed method for column crosssections with deep stiffeners. Finite element method (FEM) analysis was performed to verify the calculated load bearing strengths of the columns according to both calculation methodologies. FEM analysis confirmed the reliance of the calculated results and showed, that the load bearing strengths calculated using the newly presented methodology were ranging from 88.77% to 97.86% of load bearing strength calculated using finite element method. These results proved, that the proposed method provides an accurate load bearing strength of thin-walled columns with web stiffeners.

The noteworthy tensile plasticity and strength of CoFeSiB metallic glass fiber reinforced epoxy composites

AbstractMetallic glass fibers have high strength, poor plasticity and low Young's modulus. In this study, it was used as a reinforcement to prepare metallic glass fiber reinforced epoxy composites with different fiber volume contents (20%, 30%, 40%, and 50%). The effect of fiber volume contents on the tensile properties of the metallic glass fiber reinforced epoxy composites was studied by experiment and the finite element analysis method. The experiment and simulation results are in good agreement. The tensile strength and plasticity of the metallic glass fiber reinforced epoxy composites increase with the increase of fiber volume contents. When the fiber volume content is 40% or 50%, a sharply necking feature appeared on the fibers and exhibited improved plasticity, due to the formation of interacting and arresting events of shear bands occurring at the interface between the metallic glass fibers and the epoxy. In addition, the strain hardening due to plastic deformation of the metallic glass fibers further enhanced the tensile strength of the metallic glass fiber reinforced epoxy composites. This is a first step toward toughening the inherently brittle metallic glass fibers under tensile conditions.Highlights A novel CoFeSiB metallic glass fiber reinforced epoxy resin composite The increase of fiber volume fraction improves the tensile strength and plasticity of fiber reinforced composites. The strain hardening due to plastic deformation of the metallic glass fibers further enhanced the tensile strength of the metallic glass fiber reinforced epoxy composites.

Dependence of frequency-temperature stability on support tethers in dual-beam piezoresistive sensing MEMS resonators

This paper investigates the dependence of frequency stability over temperature on support tethers in dual-beam piezoresistive length-extensional (LE) mode microelectromechanical systems (MEMS) resonators. The designed dual-beam resonator consists of two identical single-crystal silicon beams, which are mechanically coupled and excited into vibrating in opposite phase to eliminate the inherent capacitive feedthrough signals. Both straight and folded beams are adopted as the support tethers for the reported dual-beam piezoresistive resonators. Quality factor (Q) and temperature distribution across the resonators with various support tethers are investigated by finite element method (FEM) analysis. It is found that folded beam tethers can reduce the support loss and hence improve the Q for the designed dual-beam resonator, while it comes with a tradeoff of high temperature rise on resonator body. The reported dual-beam resonator with straight beam tethers has low temperature rise on the resonator body, which is less sensitive to environmental temperature fluctuations, compared to its counterpart with folded beam tethers. Experimental results show that the fabricated dual-beam piezoresistive resonator with four straight beam tethers achieves a 0.5 ppm frequency shifts in the temperature-control chamber, which is nearly four times better than those with folded beam tethers.

Low temperature coefficient of frequency AlN Lamb wave resonator using groove structure between interdigital transducers

The lithographically tunable and small size features of Lamb wave resonators (LWRs) take a bright future for their use in high frequency narrow band filters. Resonant frequency drift due to temperature variation has a large impact on the narrower passband and a temperature coefficient of frequency (TCF) closer to 0 can broaden the stable temperature range of the resonator. This paper proposes a method of etching grooves in the area of the piezoelectric layer not covered by the Interdigital transducer (IDT) electrodes to improve the temperature stability of the Lamb resonator. Through the finite element method and theoretical analysis, the phase velocity, group velocity, and TCF dispersion curve of different modes of the resonator with groove structure were determined. The reason for the change of TCF under different normalized thicknesses of AlN was explained through the conversion of the LWR from a contour mode resonator (CMR) to a Cross-Sectional Lamé Mode Resonator. Simulation and test have shown that etching grooves have the effect of reducing TCF by adjusting the electromechanical coupling coefficient. The test shows that 205 nm-depth grooves can lower the TCF of the S0 mode IDT-Open LWR from −13.3 to −5.1 ppm/°C and S1 mode from −36.8 to −9.0 ppm/°C, respectively. The TCF of S0 and S1 mode LWRs decreased by 61.7% and 75.5%, respectively, after 205 nm groove etching. The groove etching method greatly raises the temperature stability of the LWR, enabling Lamb wave filters to operate stably over a wider temperature range.

Advancing earthquake resistance: Hybrid retrofitting of RC frames with FRP and TDS

Traditional and technological retrofitting methods have been proposed over time to enhance earthquake resistance in structures. Friction-type dampers have attracted considerable interest from both researchers and the construction industry because of their versatility in retrofitting, quick installation, and non-destructive characteristics. Moreover, the integration of damping systems with various retrofitting elements and the resulting impact of these hybrid systems on building performance have consistently been subjects of interest. This study involved the construction of three identical half-scale reinforced concrete (R.C) frames. One frame served as the reference (REF), the second was wrapped with Fiber Reinforced Polymers (FRP) material (REF-FRP), and the third was retrofitted using both FRP wrapping and the developed Technological Damper System (TDS-FRP). Quasi-static cyclic experiments were performed on the three structural frames, providing force-displacement and force-rotation relationships. The acquired data were then used to assess the damage states of the frames according to the Turkish Building Earthquake Code (TBEC 2018), and energy consumption rates were determined. Moreover, Finite Element Method (FEM) analyses were performed on REF, REF-FRP, and TDS FRP frames to derive force-displacement relationships, which were subsequently compared with experimental findings. The experiment results indicate that the horizontal load-carrying capacity of the TDS-FRP frame increased by 76 % to 122 % compared to the REF frame, while the REF-FRP frame showed a maximum increase of 14 %. Additionally, the cumulative energy consumption capacity of the REF-FRP frame increased by a maximum of 42 % compared to the REF frame, and the TDS-FRP increased between 51 % and 156 %. At a 1 % drift ratio, shear cracks at the beam ends and column-beam intersections of the REF frame were observed to be significantly reduced in the REF-FRP frame and eliminated in the TDS-FRP frame. Additionally, upon reaching a 3 % drift ratio, it was observed that the TDS-FRP frame remained within acceptable limits as per TBEC 2018, whereas the REF and REF-FRP frames exceeded the advanced damage limit. Additionally, it has been observed that the results obtained from FEM analyses coincide with the experimental results. In this context, the TDS-FRP hybrid application can be considered as an effective and alternative solution for the R.C buildings.

The Inclusion and Initial Damage Inspection of Intelligent Cementitious Materials Containing Graphene Using Electrical Resistivity Tomography (ERT)

This paper examines the theoretical foundations of electrical resistivity tomography (ERT) technology, followed by the finite element analysis method, for the positive problem and the linear back-projection (LBP) procedure for the inverse problem. The conductivity distribution image of the modeled concrete is then reconstructed, which includes one circular aggregate and the surrounding mortar. It is discovered that the conductivity obtained can be used to find the inclusive aggregate, mortar, and interfacial transition zone (ITZ). Natural aggregate and mortar have conductivities of 0.046 ms/cm and 0.115 ms/cm, respectively. Additionally, the conductivity of the ITZ, which is always regarded as the initial damage, is about 0.081 ms/cm. ERT is a cost-effective and readily available technique for determining the initial distribution of the aggregate and related ITZ. Therefore, ERT is a promising tool for determining inclusions and initial damage in concrete.

Bionanosensor utilizing single-layer graphene for the detection of iridovirus.

Iridoviruses, a group of double-stranded DNA viruses, pose a significant threat to various aquatic animals, causing substantial economic losses in aquaculture and impacting ecosystem health. Early and accurate detection of these viruses is crucial for effective disease management and control. Conventional diagnostic methods, including polymerase chain reaction (PCR) and virus isolation, often require specialized laboratories, skilled personnel, and considerable time. This highlights the need for rapid, sensitive, and cost-effective diagnostic tools for iridovirus detection. Single-layer graphene, a two-dimensional material with unique properties like high surface area, excellent electrical conductivity, and chemical stability, has emerged as a versatile platform for biosensing applications. This paper explores the potential of employing single-layer graphene in the development of a bionanosensor for the sensitive and rapid detection of iridoviruses. The aim of the present investigation is to develop a sensor by analyzing the vibrational responses of single-layer graphene sheets (SLGS) with attached microorganisms. Graphene-based virus sensors typically rely on the interaction between the virus and the graphene surface, which lead to changes in the frequency response of graphene. This change is measured and used to detect the presence of the virus. Its high surface-to-volume ratio and sensitivity to changes in its frequency make it a highly sensitive platform for virus detection. We employ finite element method (FEM) analysis to model the sensor's performance and optimize its design parameters. The simulation results highlight the sensor's potential for achieving high sensitivity and rapid detection of iridovirus. Bridged and simply supported with roller support boundary conditions applied at the ends of SLG structure. Simulations have been performed to see how SLG behaves when used as sensors. A single-layer graphene armchair SLG (5,5) with 50-nm length exhibits its highest frequency vibration at 8.66 × 106 Hz, with a mass of 1.2786 Zg. In contrast, a zigzag-SLG with a (18,0) configuration has its lowest frequency vibration at 2.82 × 105 Hz. This aids in comprehending the thresholds of detection and the influence of factors such as size, and boundary conditions on sensor effectiveness. These biosensors can be especially helpful in biological sciences and the medical field since they can considerably improve the treatment of patients, cancer early diagnosis, and pathogen identification when used in clinical environments.

Microstructural analysis of titanium alloys based on high-temperature phase reconstruction

The microstructural evolution of titanium alloys under high-temperature conditions plays a key role in determining their mechanical properties and hot working behavior. This research presents an advanced method for calibrating β phase reconstruction software using in situ testing on Grade 2 titanium, which achieves accurate reconstruction of the parent β phase microstructure. In addition, unique microstructural observations in the forging of Ti-6246 titanium alloy are highlighted, demonstrating the influence of deformation parameters on the resulting β phase grain structures. Using advanced techniques such as electron backscatter diffraction and Burgers orientation relationship-based software, the research elucidates the behavior of these phases under varying thermal and deformation conditions. In Grade 2 titanium, significant grain growth and phase transformation dynamics were observed upon heating beyond the β-transus temperature during in situ calibration of β phase reconstruction software. The analysis demonstrates the effectiveness of the software in precise reconstructing the parent β phase microstructure based on the orientation of the inherited αs phase. Furthermore, the evaluation of hot forming parameters in Ti-6246 alloy shows the influence of deformation temperature and strain rate on the resulting microstructure. Finite element method analysis coupled with dynamic material modeling elucidates the distribution of temperature, strain rate, and effective strain during forging, which aids in the qualitative assessment of hot workability. Microstructural observations in Ti-6246 alloy forging highlight the presence of elongated colonies of αs phase precipitates, indicative of localized strain intensities and deformation temperatures. In addition, EBSD analysis coupled with β phase reconstruction reveals distinct microstructural features in different regions of the forging. In particular, regions subjected to higher strain rates exhibit elongated β phase grains with pronounced disorientation gradients, suggesting intense deformation. Conversely, optimal forging conditions lead to the appearance of unreinforced axisymmetric β phase grains, indicating dynamic recovery processes. Pole figure analysis further emphasizes the Burgers crystallographic relationship between the αs and β phases, confirming that deformation during forging occurs exclusively within the β phase. These results provide valuable insights into the microstructural evolution in titanium alloys under high-temperature conditions, which are essential for optimizing hot working processes and improving mechanical properties.Graphical abstract

Investigation on the biaxial tensile testing method for metal foil using cruciform specimen

The assessment of mechanical properties of metal foil under complicated stress states poses a considerable challenge, requiring the development of new testing methods and the optimization of new specimen geometry. In this research, the biaxial tensile method and specimen shape were designed and optimized by using simulation and experiment. It is determined that the strain measurement area can be suggested as the central area of 0.6 to 0.8 times the arm width. The influence of different parameters on the tensile results of cruciform specimens was comprehensively evaluated by finite element method and multi-factor analysis. The results indicate that the number of slits markedly impacts the stress–strain uniformity and shear stress in the central region, followed by the slit length. The effect of the arm width and the slit width is comparable, more influential than the corner radius. According to the analyzed results and application requirements, a four-axis independently driven biaxial tensile test machine for small scale samples was fabricated. During the biaxial tension, the center point offset of the specimen remains within ±0.01 mm. The displacement and load synchronization errors do not exceed 0.01 mm and 50 N, respectively, facilitating the precise control of four-axis synchronization. Conclusively, cruciform specimens featuring diverse geometric characteristics were designed for industrial pure titanium, 304 stainless steel, and Inconel 718 superalloy with thickness of less than 0.3 mm. The biaxial tensile tests were performed to delineate the yield loci, revealing notable anisotropy and size effect. The validation confirms the suitability of the testing method and optimized cruciform specimens for conducting biaxial tensile mechanical properties testing on metal foils characterized by diverse types and thicknesses.