Continuous Beam Research Articles

Computer-Vision-Aided Deflection Influences Line Identification of Concrete Bridge Enhanced by Edge Detection and Time-Domain Forward Inference

To enhance the accuracy and efficiency of the deflection response measurement of concrete bridges with a non-contact scheme and address the ill-conditioned nature of the inverse problem in influence line (IL) identification, this study introduces a computer-vision-aided deflection IL identification method that integrates edge detection and time-domain forward inference (TDFI). The methodology proposed in this research leverages computer vision technology with edge detection to surpass traditional contact-based measurement methods, greatly enhancing the operational efficiency and applicability of IL identification and, in particular, addressing the challenge of accurately measuring small deflections in concrete bridges. To mitigate the limitations of the Lucas–Kanade (LK) optical flow method, such as unclear feature points within the camera’s field of view and occasional point loss in certain video frames, an edge detection technique is employed to identify maximum values in the first-order derivatives of the image, creating virtual tracking points at the bridge edges through image processing. By precisely defining the bridge boundaries, only the essential structural attributes are preserved to enhance the reliability of minimal deflection deformations under vehicular loads. To tackle the ill-posed nature of the inverse problem, a TDFI model is introduced to identify IL, recursively capturing the static bridge response generated by the bridge under the influence of successive axles of a multi-axle vehicle. The IL is then computed by dividing the response by the weight of the preceding axle. Furthermore, an axle weight ratio reduction coefficient is proposed to mitigate noise amplification issues, ensuring that the weight of the preceding axle surpasses that of any other axle. To validate the accuracy and robustness of the proposed method, it is applied to numerical examples of a simply supported concrete beam, indoor experiments on a similar beam, and field tests on a three-span continuous concrete beam bridge.

Experiment and Numerical simulation on Bearing Capacity of Partial Steel-ultra-high-performance Concrete Continuous Composite beams

Due to high strength, toughness and durability, ultra-high-performance concrete (UHPC) can be applied in replacing the cracked concrete slab in the negative moment region of newly built steel-ordinary concrete (OC) continuous composite beams, as well as in repairing old composite beams. To investigate the failure mode, crack propagation, stiffness degradation and bearing capacity of the partial steel-UHPC continuous composite beam, a test model with an UHPC slab over the negative moment region were designed and fabricated to compare with a steel-OC model with the same conditions. Similar failure mode was observed in the loading test of two models. Nevertheless, the maximum crack width in the UHPC slab is only 0.17mm, much smaller than that in the OC slab. Compared with the steel-OC composite beam, vertical deflection of the partial steel-UHPC composite beam decreases by 32.7%, and its cracking load and ultimate bearing capacity increase by 50% and 6.4%, respectively. The results show that the substitution of the OC with the UHPC in the negative bending moment area significantly improves the crack resistance, delays the crack propagation, increases the bending stiffness, and improves the working performance of composite beams with cracks, displaying good advantages in economy and in reality. Parametric analysis demonstrates that the height of steel beam is the most important factor, and cross section of the steel beam is suggested to be given priority in design so as to take advantages of partial steel-UHPC composite beams. The research also provides an option for the repair of old concrete slabs in steel-OC continuous composite beams.

A Dual-Band Leaky Wave Antenna With Dual-Bi-Directional Continuous Beam Scanning for Large Space Radiation Coverage

A Dual-Band Leaky Wave Antenna With Dual-Bi-Directional Continuous Beam Scanning for Large Space Radiation Coverage

Structural performance of split orthogonal beam joints in continuous beam‐type circular concrete‐filled steel tubular beam‐to‐column connections

AbstractA continuous beam‐type connection has been proposed as a new type of concrete‐filled steel tubular beam‐to‐column connection without a diaphragm exhibits good seismic performance. However, in a 2‐way configuration, the performance of the connection in a direction orthogonal to the continuous beam may be suboptimal due to beam splitting. In this study, a new detail of a split orthogonal beam joint was proposed and 4 specimens were constructed and tested under quasi‐static conditions. All the specimens attained the full‐plastic flexural strength for the beams and exhibited a stable inelastic behavior. The specimen in which the depth of the orthogonal continuous beam was 100 mm greater than that of the split beam exhibited good inelastic cyclic behavior, whereas two other specimens with a split beam exhibited slipping and pinching. Minor fractures were observed in the tube wall; however, the strength and stiffness did not deteriorate significantly, though a slight pinched hysteresis was observed. In addition, a finite element analysis was conducted. The split beam was largely rotationally constrained by the bearing pressure of the concrete above and/or below the beam flange. If the split beam's flange was sufficiently inserted into the connection panel, the stiffness and strength were ensured.

Simplified site response analysis for regional seismic risk assessments

Seismic risk assessment on a regional scale requires an estimation of ground motion intensity and its spatial variation over large geographical areas. This task is particularly challenging in the presence of very soft soil deposits where significant amplification occurs at specific frequencies that are often referred to as local resonances. It is often not feasible to conduct a nonlinear site response analysis at thousands of sites of interest across a region such as an urban area due to the computational effort involved and the required detailed information on soil profiles at each site. Thus, in regional seismic risk analyses the hazard is typically represented by a field of response spectral ordinates estimated by ground motion models. This study proposes a simplified site response analysis procedure to improve the characterization of spectral ordinates to be used in regional seismic risk assessments. In the proposed procedure, reduced-order models are used to conduct site response analysis using very few parameters to transform response spectra at rock outcrop into response spectra at the surface of each of the sites. A particular emphasis is given to soft-soil sites characterized by low shear-wave velocities overlaid on rock or firm soils. A non-uniform continuous shear beam model with a parabolic variation of shear modulus along the depth and modal damping is used in combination with Random Vibration Theory. It is shown that the proposed approach provides better estimates than those of ground motion models or physics-based ground motion simulation models which often cannot capture the local resonances. Site-specific validation of the shear beam model and overall simplified site response analysis is performed at four soft-soil sites in San Francisco, California. Despite its simplicity, it is shown that the proposed procedure adequately captures the amplitudes and spectral shapes of the motions. It is also shown that in conjunction with ground motion models or physics-based models, the proposed simplified site response analysis procedure can be used to efficiently simulate the seismic hazard on a regional scale through an example of a regional seismic hazard analysis of 160 softer soil sites in Downtown San Francisco during the Loma Prieta earthquake.

Development of a novel crack-resistance technique for concrete slab in the hogging moment region of continuous composite beam

Composite steel-concrete beams offer distinct mechanical advantages. However, concrete cracking in the hogging moment region limits the composite performance of the material. This study presents an innovative technique for enhancing the crack resistance of continuous steel-concrete composite beams, which involves the prestressing of the concrete slab in the hogging moment region through post-tensioning. Following the completion of the concrete slab in the sagging moment region, the prestress is released, thereby preserving pre-compression stress in the hogging moment region without the need for long-term prestressing. This technique is enhanced using uplift-restricted and slip-free connectors, which improve the efficiency of pre-stress introduction. Experimental tests were conducted on composite beams employing this novel technique, alongside numerical simulations. The results indicated that the proposed technique significantly mitigated concrete cracking in the hogging moment region. Specifically, the cracking load of the specimen using the new technique increased by 467 % compared to the traditional composite beam specimen, accompanied by a substantial reduction in both the quantity and width of cracks. Other primary mechanical performance indicators remained relatively similar; however, the new technique exhibited a 14 % increase in the ductility coefficient compared with the traditional method. Additionally, this technique influenced interface slip, moment redistribution, and strain response along the cross-section in both the hogging and sagging moment regions. The numerical results aligned closely with the experimental data, confirming their accuracy and effectiveness. The simulations provided solutions for various construction stages by incorporating different connection constitutive models with adequate precision. A parametric analysis was conducted, revealing a design method for the innovative technique.

Seismic response study of multi-span continuous beam bridges near faults considering permanent displacement attenuation effects

The fling-step effect caused by near-fault ground motion induces a step-like permanent displacement of the ground surface, which decays sharply with increasing fault distance, leading to varying degrees of ground motion at each supporting point of the bridge structure. In this context, multi-span long-span bridges exhibit echelon displacement of the main beam and a more complex internal force response compared to ordinary bridges. To investigate the seismic response characteristics of multi-span long-span continuous girder bridges under near-fault ground motion, this study is based on the permanent displacement attenuation model. The main bridge of the Hongyazi Yellow River Bridge in Shizuishan City, consisting of 16 spans, is taken as the research object. Using OpenSees software, a finite element model for the dynamic analysis of the multi-span long-span continuous girder bridge was established, and its structural dynamic characteristics were compared with the natural vibration test of the actual bridge. Based on simulated ground motions that consider the permanent displacement attenuation effect and spatial variability, the seismic response of the key components of the near-fault multi-span long-span continuous beam bridge is examined. The results indicate that under near-fault ground motion considering the attenuation effect of permanent displacement, the main girder of multi-span long-span bridges frequently deviates from the axis in different directions, ultimately resulting in residual deformation of the main girder post-earthquake. The permanent displacement attenuation effect increases the maximum bending moment response at the pier bottom and causes uneven internal force distribution in the bridge. Ignoring this effect can lead to overestimation of bearing deformation.

Determining the carbon detection limit with magnetic sector dynamic secondary ion mass spectrometry (SIMS)

Dynamic SIMS is often used to evaluate the concentration of impurities in solids because of its high sensitivity, depth profiling capabilities, good depth resolution, and high throughput. Continuous ion beam sputtering with a high-density primary beam provides high sensitivity and reduces the background contribution from residual gases within the analytical chamber. Dynamic SIMS experiments performed with several magnetic sector instruments using various sputtering rate conditions demonstrated a slow decrease of the carbon detection limit with the increase of sputtering rate (SR), when it was varied by changing the sputtering beam density. The dependence data, within the scatter limits, can be fit by a power function of SR with the exponent of about −1/2. The observed detection-limit-dependence curve is common for magnetic sector SIMS instruments, owing to contamination and the design of the analytical chamber. The depth resolution of light-element SIMS analysis (except for oxygen) performed using Cs+ sputtering is limited and cannot be improved by reducing the impact energy of the sputtering beam. A segregation-type depth profile with a long trailing edge was observed in the B, C, and N depth profiles when Cs+ sputtering was employed under ultra-high vacuum conditions. This effect is plausibly associated with preferential sputtering owing to the difference in the surface binding energy, along with the large difference in the mass of the interacting atoms within the collision cascade during sputtering. The depth resolution improved with surface oxidation when Cs + sputtering was combined with backfilling of the analytical chamber using O2. The analytical chamber backfilled with oxygen can be sufficiently replaced with a very low-impact energy-focused oxygen beam, enabling simultaneous oxygen and cesium co-sputtering SIMS analysis. The practical feasibility of using a co-sputtering with focused Cs+ and O2+ sputtering beams to achieve a high depth-resolution for carbon analysis under ultrahigh vacuum conditions was demonstrated.

A tunable 3×5 Nolen matrix for sidelobe-reduced and beamforming applications

A methodology of designing a 3×5 Nolen matrix with non-uniform power distribution is proposed in this paper. Several tunable phase shifters are designed to realize the capability of continuous beam steering. Additionally, two power dividers are integrated with a 3×5 Nolen matrix to produce the desired non-uniform power distribution, thereby reducing the sidelobe levels. In order to establish the appropriate power divider ratios, this paper thoroughly examines the correlation between power ratio at each port and different loss scenarios as well as Chebyshev distribution. An experimental Nolen matrix prototype has been designed and fabricated to confirm the efficacy of our proposed approach. The fabricated 3×5 Nolen matrix prototype offers continuous beam steering and achieves sidelobe levels below −22 dB.

Study of the dynamic response of an offshore continuous beam bridge under nonlinear wave and scour

The study highlights the critical factors and findings regarding bridge damage susceptibility during typhoons and hurricanes, primarily due to extreme waves, scour, and storm surges. While existing research has extensively studied bridges' responses to either extreme waves or scour individually, their combined effects have not been sufficiently explored. Experiments were conducted on a scaled two-span bridge to examine its behavior under simultaneous wave and scour conditions. Results from these experiments indicate that as scour depth increases, there is a corresponding escalation in displacement of the bridge pier, acceleration of the bearing platform, and strain along the pile foundation. To further investigate these dynamics, fluid-structure interaction analysis was employed, revealing significant insights. Notably, the study found that wave height exerts a substantial influence on wave load. For instance, at a wave height of 6 m, the average peak horizontal wave load on bridge piers was 2.48 times higher than at 3 m wave height. Moreover, local scour was identified as a critical factor reducing the bearing capacity of pile foundations, thereby significantly impacting the bridge's dynamic response to nonlinear waves. Under identical wave conditions, varying scour depths (3 m, 6 m, 9 m, and 12 m) resulted in increases in peak lateral displacements at the pier top compared to non-scouring conditions. The study concludes by emphasizing the increasing risk posed to pile foundations with deeper scour depths, particularly under stronger wave conditions. Consequently, there is a crucial need to enhance the resilience of offshore bridges against these dual hazards through advanced design and protective measures.

Silicone Rubber-Packaged FBG Sensing Information and SSI-COV-Recognized Modal Parameters Motivated Damage Identification in Pipe Structures

Pipes are the main structures serving as the lifeline for oil and gas transportation. However, they are prone to cracks, holes and other damages due to harsh working environments, which can lead to leakage incidents and result in significant economic losses. Therefore, the development of structural health monitoring systems with advanced online diagnostic methods is of great importance for identifying local damages and assessing the safety state of pipe structures. These efforts can guide rapid repairs and ensure the continuous, efficient and cost-effective transportation of oil and gas resources. To address this problem, this paper proposes the development of a pipe monitoring system based on quasi-distributed fiber Bragg grating (FBG) sensing technology. The SSI-COV method is employed to process the sensor responses and extract the modal parameters of the structure. Based on this foundation, an enhanced damage identification index is proposed, which mitigates the effects of support and excitation positions on damage identification. The pipe structure can be regarded as a continuous super-statical beam, and based on its structural symmetry, a unit structure, specifically a stainless-steel pipe with fixed ends, is regarded as the experimental subject. Impact experiments have been conducted to analyze its behavior in both undamaged and damaged states. The research indicates that by using the proposed modal parameter identification method and the ASMDI damage index, ASMDI exhibits peak values at damage locations of the pipe structure. This allows for the identification of structural damage with high accuracy, fast processing efficiency and strong robustness. The study provides an effective and reliable damage diagnosis method, which can contribute to the refinement and visualization of pipe structural health monitoring systems.

A composite microstrip line and leaky wave antenna structure with self-diplexing characteristic

A novel structure is proposed for the dual-band self-diplexing integration of microstrip line and leaky wave antenna (LWA). Through introducing a mode selective transmission line (MSTL) to the antenna, the autonomous transition between transmission modes at varying operating frequencies is thus achieved. At the high-frequency band, such proposed antenna in the quasi-TE10 mode, the periodic slots, and patches are used as LWA. Meanwhile, at the low-frequency band, the baseband signal with quasi-TEM mode can be transmitted effectively. These experimental results demonstrate that this design strategy benefits the realization of transmission with an insertion loss of less than 3 dB below 5.5 GHz. Furthermore, this antenna enables continuous beam scanning of −1 space harmonics from 10.5 to 15.5 GHz, with a beam direction sweeping from −75° to + 54°. This study innovatively employs MSTL structure to solve the problem of radio frequency (RF) and baseband links operating independently in traditional communication systems. It provides a promising solution for multi-functional integrated applications in future wireless communications.

Advances and applications of the strut-and-tie method in reinforced concrete design: A state-of-the-art review

The Strut-and-Tie Method (STM) is a versatile and powerful approach widely used in the design and analysis of reinforced concrete structures, particularly in regions with complex stress distributions and discontinuities. This review article delves into the theoretical foundations, practical applications, and experimental validations of the STM. The article begins by exploring the fundamental principles of the STM and its historical development, with a focus on its application in predicting the capacity of reinforced concrete members. Additionally, the STM efficacy in designing deep beams and comparisons with other analytical methods are thoroughly examined. Notably, the review includes a discussion on the application of STM in concrete beams, highlighting its ability to accurately predict capacity. Several studies investigating the behavior of reinforced concrete deep beams with openings, shear-strengthened deep beams, and continuous deep beams using the STM approach are critically analyzed, providing valuable insights into its reliability and practicality. Furthermore, the review delves into advancements in computational tools and finite element analyses that have been integrated with the STM, offering a more comprehensive and robust approach to design and analysis. The article also evaluates practical applications of STM in engineering scenarios, such as the design of bridge pier caps and complex regions, showcasing its versatility and adaptability. In conclusion, this review underscores the pivotal role of the Strut-and-Tie Method in modern reinforced concrete design and analysis. It serves as a valuable resource for engineers, researchers, and practitioners seeking to apply this method effectively in various structural configurations and challenging scenarios. Ultimately, the article emphasizes the significance of STM as a reliable and efficient tool for optimizing the design and ensuring the safety and performance of reinforced concrete structures.

Research on Moment Redistribution of Prestressed Steel Reinforced Concrete Continuous Beams

Research on Moment Redistribution of Prestressed Steel Reinforced Concrete Continuous Beams

Terahertz single/dual beam scanning with tunable field of view by cascaded metasurfaces

Dynamic beam scanning with a dynamically tunable beam number, beam direction, and beam polarization remains a challenge in the terahertz gap, which is urgently needed for terahertz radar, next-generation wireless communication, and imaging applications. Different from programmable metasurfaces with element-level phase control, the beam direction is dynamically controlled by two cascaded all-dielectric metasurfaces during in-plane rotation. For a pair of circularly polarized beams with opposite handedness, the scanning field of view (FOV) can be the same or different according to the independent phase modulation in both layers and for both polarization states. Switchable single-beam and dual-beam scanning is achieved by controlling the incident polarization, which covers the ±60° FOV at 0.291 THz with an angular step of 1° and an average gain of 16.2 dBi. The output beam is quasi-circular polarized with an average ellipticity of 0.83. Single beam scanning along a Fibonacci spiral trajectory and dual beam scanning along symmetric and asymmetric trajectories are experimentally validated. Different beam scanning processes are recorded using a terahertz camera, which show good agreement with the theoretical prediction. The wide field-of-view continuous beam scanning with a switchable number of beams and a flexible FOV may have a significant impact on the development of terahertz radar and terahertz intelligent antennas.

Moment redistribution capacity in prestressed concrete continuous beams

In prestressed concrete continuous beams, building code provisions often allow for a reduction in the moment at a critical section (calculated through elastic analysis). This reduction is permitted as long as the moments in all other sections are adjusted to maintain equilibrium and support the designated loads. However, the allowable moment redistribution percentage (MRP) for prestressed concrete beams (PCBs) remains a topic of debate. Many codes currently assign a similar MRP limitation to both PCBs and reinforced concrete beams (RCBs). This approach might be over-simplistic for PCBs due to their unique behaviour. A method for identifying the maximum available MRP is proposed in this article. An in-depth study was conducted on the maximum available MRP of PCBs based on calibrated finite-element models. The results showed that parameters such as the passive reinforcement ratio, steel yield strength, slenderness ratio, eccentricity of prestressing tendons, concrete grade and load pattern, which are not considered in the codes, influence the maximum available MRP to an extent. Using the same permissible MRP as RCBs may thus be inappropriate. An equation is proposed to estimate the maximum available MRP for PCBs.

A Comparative Study of Single-Chain and Multi-Chain MCMC Algorithms for Bayesian Model Updating-Based Structural Damage Detection

Bayesian model updating has received considerable attention and has been extensively used in structural damage detection. It provides a rigorous statistical framework for realizing structural system identification and characterizing uncertainties associated with modeling and measurements. The Markov Chain Monte Carlo (MCMC) is a promising tool for inferring the posterior distribution of model parameters to avoid the intractable evaluation of multi-dimensional integration. However, the efficacy of most MCMC techniques suffers from the curse of parameter dimension, which restricts the application of Bayesian model updating to the damage detection of large-scale systems. In addition, there are several MCMC techniques that require users to properly choose application-specific models, based on the understanding of algorithm mechanisms and limitations. As seen in the literature, there is a lack of comprehensive work that investigates the performances of various MCMC algorithms in their application of structural damage detection. In this study, the Differential Evolutionary Adaptive Metropolis (DREAM), a multi-chain MCMC, is explored and adapted to Bayesian model updating. This paper illustrates how DREAM is used for model updating with many uncertainty parameters (i.e., 40 parameters). Furthermore, the study provides a tutorial to users who may be less experienced with Bayesian model updating and MCMC. Two advanced single-chain MCMC algorithms, namely, the Delayed Rejection Adaptive Metropolis (DRAM) and Transitional Markov Chain Monte Carlo (TMCMC), and DREAM are elaborately introduced to allow practitioners to understand better the concepts and practical implementations. Their performances in model updating and damage detection are compared through three different engineering applications with increased complexity, e.g., a forty-story shear building, a two-span continuous steel beam, and a large-scale steel pedestrian bridge.

Full-scale experimental study on tribological performance of FPBs for highway bridges with various solid lubricants under fast loading

Friction pendulum bearings (FPBs) have proven to be effective for the seismic isolation of highway bridges. Previous studies often employed scaled model shaking table tests to investigate dynamic responses of the structures or quasi-static tests to assess the hysteretic performance of FPBs. However, it is noteworthy that the stress on the friction surface is reduced due to the size effect in scaled model in shaking table tests, while quasi-static tests of prototype bearings cannot simulate the sliding velocity experienced during seismic events, which is a sensitive parameter for the performance of FPBs with solid lubricant plates. Research on the performance of full-scale FPBs under fast frictional loading is very limited. This paper addresses this knowledge gap by studying the velocity demand for a highway bridge with FPBs and conducting fast sliding performance tests using full-scale FPBs. The results indicate that under a 0.2 g PGA earthquake, the velocity demand for FPBs can reach 0.5 m/s. Through testing full-scale FPBs at various loading speeds, it was found that solid lubricant plates by UHMWPE material exhibit poor thermal stability during wear tests, solid lubricant plates by PTFE material lack sufficient tangential tear strength under fast loading, and solid lubricant plates by PET material show good wear resistance but have a high breakaway force and levered maximum force during the running-in stage. Subsequently, this study developed ultra-high performance friction plate (UHPF) as the solid lubricant for FPBs, achieving ideal hysteretic performance under fast loading. The full-scale FPB specimens in this paper are the ones manufactured for the continuous beam bridges in the Shenzhen-Zhongshan Sea-crossing Link project in China. The dimensions of the bearing, axial load, and loading speed is much more stringent than those in previous FPB tests, providing results that are highly important for engineering applications.

Time-convolutional network with joint time-frequency domain loss based on arithmetic optimization algorithm for dynamic response reconstruction

Structural Health Monitoring (SHM) systems provide extensive data on in-service bridges, which is crucial for evaluating structural performance. However, data loss frequently occurs due to environmental factors and technical failures. Although missing data reconstruction problem has been largely studied, the accuracy of response reconstruction in the frequency domain is often overlooked. To address this issue, this study proposes to integrate a time-frequency joint loss function within an Arithmetic Optimization Algorithm-Temporal Convolutional Network (AOA-TCN), which leverages temporal and spatial dependencies among measurement points to reconstruct missing dynamic deflection data. The time-frequency joint loss function is enhanced with linear decay weights to increase sensitivity to low-order modal contributions, with an adaptive weighting mechanism balancing loss contributions from time and frequency domains. These adaptive weight parameters are optimized through AOA to enhance the TCN's generalizability. The feasibility and effectiveness of the proposed method are first demonstrated using simulated dynamic deflection data of a finite element model of a continuous beam bridge, and then experimentally verified on a real-world simply-supported beam bridge. The results indicate that the proposed method achieves higher data reconstruction accuracy and more precise modal analysis results compared to existing methods. The Modal Assurance Criterion (MAC) between mode shapes identified using measured data and reconstructed response reached 96.9 %, proving that the proposed method is capable of reconstructing the missing structural response while retaining its frequency-domain information, which is valuable for structural integrity assessment based on modal parameter identification of operational bridges.

A semi-analytical method based on the Green's function for the laser melting process of the metal materials

Thermal responses of the metal materials subjected to intense laser irradiation are complicated due to the phase change in the melting process. In order to simplify this problem, previous studies usually ignored the liquid phase or took the usage of finite element method, which limited the achievement of theoretical breakthroughs. In the present study, a one-dimensional heat transfer model with consideration of phase change was established to describe the melting process of the metal materials caused by a constant intense laser beam. The governing equations with three domains were constructed in the piecewise form: the liquid phase region (melted already), the solid phase region (unmelted yet) and the melting region. The limited discretization method was employed to describe the moving of the soli-liquid interface and the energy exchange. The piecewise governing equations in liquid and solid region were solved separately and analytically by means of the Green's function method, and the calculation result was verified by the finite element simulation. The results of the analytical model were in good agreement with those of the finite element simulation, and the maximal prediction errors of the temperature field prediction between the theoretical model and FE simulation is limited to 2.8 %. In addition, the influences of heat source intensity, material heat conductivity, latent heat on the melting process were discussed in detail. The analytical and simulation results reveal that the semi-analytical solution in piecewise for 1-D laser melting process can be successfully used to reflect the dynamic temperature response of the metal materials and the movement of the solid-liquid interface. This work is of guiding significance for the analytical solution of the multi-dimensional melting process of the metal materials under the fixed and continuous laser beams.