Nonlinear Finite Element Method Research Articles

Thermal Induced Interface Mechanical Response Analysis of SMT Lead-Free Solder Joint and Its Adaptive Optimization.

Surface mount technology (SMT) plays an important role in integrated circuits, but due to thermal stress alternation caused by temperature cycling, it tends to have thermo-mechanical reliability problems. At the same time, considering the environmental and health problems of lead (Pb)-based solders, the electronics industry has turned to lead-free solders, such as ternary alloy Sn-3Ag-0.5Cu (SAC305). As lead-free solders exhibit visco-plastic mechanical properties significantly affected by temperature, their thermo-mechanical reliability has received considerable attention. In this study, the interface delamination of an SMT solder joint using a SAC305 alloy under temperature cycling has been analyzed by the nonlinear finite element method. The results indicate that the highest contact pressure at the four corners of the termination/solder horizontal interface means that delamination is most likely to occur, followed by the y-direction side region of the solder/land interface and the top arc region of the termination/solder vertical interface. It should be noted that in order to keep the shape of the solder joint in the finite element model consistent with the actual situation after the reflow process, a minimum energy-based morphology evolution method has been incorporated into the established finite element model. Eventually, an Improved Efficient Global Optimization (IEGO) method was used to optimize the geometry of the SMT solder joint in order to reduce the contact pressure at critical points and critical regions. The optimization result shows that the contact pressure at the critical points and at the critical regions decreases significantly, which also means that the probability of thermal-induced delamination decreases.

Computationally aware estimation of ultimate strength reduction of stiffened panels caused by welding residual stress: From finite element to data-driven methods

Ultimate limit state (ULS) assessment examines the maximum load-carrying capacity of structures considering inelastic buckling failure. Contrary to the traditional allowable stress principle which is mainly based on experiences, the ULS assessment focuses on explicitly evaluating the structural safety margin and thus enables a consistent level of safety/risk between conventional and novel structural designs. Modern structures are usually designed as a network of plates and stiffeners (e.g., ship structures, offshore and onshore wind turbine, and land-based bridge) joined by welding which induces a residual stress field. Hence, predicting the ultimate strength reduction of stiffened panels caused by welding residual stress is a crucial problem addressed by many scholars with different approaches, among which the Nonlinear Finite Element Method (NLFEM) is the prevailing approach within the community of structural engineering. Unfortunately, the NLFEM has a high computational requirement which prevents its use in the design, appraisal, and optimisation phases of stiffened panels. To well approximate the nonlinear finite element method, a data-driven method is proposed in this paper, with a functional which is computationally expensive to build but computationally inexpensive to use allowing its application at design stage. Results obtained in different (i.e., interpolation and extrapolation) scenarios using data generated by a state-of-the-art NLFEM on a series of stiffened panels will support the proposed method.

Research on Mooring System Design for Kulluk Platform in Arctic Region

Mooring system design of a floating offshore structure in the arctic region is considered to be extremely important. This paper aims at investigating an optimal mooring system for the Kulluk platform operating in the Beaufort Sea, which has ice-free and ice-covered conditions during the whole year time. In order to complete the layout design of the mooring system to satisfy the year-round operation, both the effect of wave loads and ice loads should be considered. The research establishes a coupled numerical production system composed of the Kulluk platform and mooring system. Wave load is solved by potential flow theory. The slender finite element method is used to compute the tension of the mooring system. The nonlinear finite element method, discrete element method, and empirical formula are compared to analyze ice load. Finally, the discrete element method is selected for the analysis of the Kulluk, and the simulated results are compared reasonably with the field data. When studying the mooring line configurations, quantitative time-domain analysis is carried out, including tension of mooring lines and the motions of the platform under different working conditions. The research work in this paper will provide a reference for the optimal design of the mooring system of the platform operating in the Arctic Sea.

Mechanisms and Evolution of Cracks in Prestressed Concrete Sleepers Exposed to Time-Dependent Actions

Railway sleepers are an important component of track systems, which can be manufactured by timber, concrete, steel and any other engineered materials. They serve as rail supports and transfer loads from trains to substructures of track systems. In railway networks worldwide, prestressed concrete sleepers are more common than other material types because of their cost-efficacy, environmental friendliness, higher stability and performance, and durability. However, certain types of damage can still appear due to diverse load spectra and aggressive environmental conditions. The causes of cracking observed in prestressed concrete sleepers are usually induced by impact loads. The most affected sections are at the midspan and the rail-seat area of sleepers. Over a long term, time-dependent actions also affect the structural performance of prestressed concrete sleepers. This paper intends to determine the time-dependent crack phenomena in prestressed concrete sleepers under static conditions. Nonlinear finite element method (FEM) has been developed and validated by full-scale experimental tests of prestressed concrete sleepers in accordance with EN13230. In this study, equivalent losses of prestress as a result from time-dependent actions and resultant behaviours are considered. Their influences on crack initiation and propagation in prestressed concrete sleepers have been demonstrated. The results exhibit that the crack simulation can accurately predict the cracking behaviours and the time-dependent behaviour of prestressed concrete sleepers. This insight is critically essential to experimental load rating prediction, that can appropriately estimate the remaining life of aged railway concrete sleepers exposed to time-dependent actions.

Collision-accidental limit states-based safety studies for a LNG-fuelled containership

Liquefied natural gas (LNG) is an increasingly popular fuel alternative of ships for reducing greenhouse gas emissions. The interest in LNG fuel propulsion systems is rapidly growing, yet certain important safety design and engineering issues remain poorly constrained. The safety of LNG-fuelled ships must be assessed in terms of the potential structural damage owing to collision accidents and resulting LNG spills, especially for ship types that store the LNG storage tank within the cargo hold. In this paper, accidental limit state (ALS) based safety assessment for LNG-fuelled containership structures using nonlinear finite element methods is studied at the most unfavourable scenario of collisions between a striking ship's bow and a struck ship's LNG fuel tank, where the struck ship is in full load condition at a standstill, while the striking ship of the same size as the struck ship has different loading conditions in the ballast load condition, 50% partial load condition and full load condition, with varying collision speed at 0.5, 3, 6 and 9 knots. A hypothetical 9,000 TEU (Twenty-foot Equivalent Unit) LNG-fuelled containership was designed in accordance with the requirements for the international gas fuel transport standards, accommodating a membrane-type LNG fuel tank located amidship. It is found from the present study that inner side hull structures of the struck ship can be damaged in ship-ship collisions, and the current industrial guidelines for LNG fuel tank designs are required to amend to apply for LNG-fuelled ships.

Thermally nonlinear non-Fourier piezoelectric thermoelasticity problems with temperature-dependent elastic constants and thermal conductivity and nonlinear finite element analysis

In non-isothermal conditions, numerous experimental and theoretical investigations reveal that the elastic constants and thermal conductivity in piezoelectric solids depend on temperature distribution. This work aims to investigate thermally nonlinear non-Fourier piezoelectric thermoelasticity problems with temperature-dependent elastic constants and thermal conductivity. The nonlinear time-domain finite element method is developed to directly solve nonlinear finite element governing equations, which maximally avoids the precision losses within the applications of the integrated transformation method. As a numerical example, the developed method is applied to analyze nonlinear transient thermo-electromechanical responses of a two-dimensional orthotropic piezoelectric plate of crystal class mm2. The achieved results reveal that temperature-dependent thermal conductivity and elastic constants remarkably affect the structural dynamic responses, whilst thermal wave or elastic wave will travel faster and the electrical energy harvesting ability is significantly elevated.

Study on residual strength and life prediction of corroded tubing based on thermal-mechanical coupling XFEM

Based on the experimental results of the stress-strain constitutive relationship, thermal expansion coefficient and thermal conductivity for P110S tubing material, a three-dimensional thermal-mechanical coupling mechanical model of P110S tubing with uniform, local and pitting corrosion is established by using nonlinear finite element method with due consideration on the physical nonlinearity of the corroded tubing and the geometric nonlinearity caused by large deformation comprehensively in this paper. The model is verified using full-scale burst test data. Based on the verified model, the burst mechanical behavior and burst strength of corroded tubing under thermal-mechanical coupling were simulated by adopting the XFEM method and burst failure criterion based on damage mechanics evolution, by which the investigation on burst mechanical behavior of P110S tubing wih pitting corrosion is paid the most attention. Based on the sensitivity analysis results of residual strength of corroded tubing and the corrosion test results, a prediction model of the residual strength for P110S corroded tubing is established by using the 1stOpt software and universal global optimization (UGO) algorithm, by which the evaluation method of service life for P110S corroded tubing is proposed.

Finite Element Analysis of the Limit Load of Straight Pipes with Local Wall-Thinning Defects under Complex Loads

Local wall thinning is a common defect on the surface of pipelines, which can cause damage to the pipeline under complex pipeline loads. Based on the study on the limit load of straight pipes with defects, the nonlinear finite element method was used to analyze the limit load of straight pipes with local wall-thinning defects under internal pressure, bending moment, torque, axial force, and their combinations, and the empirical limit-load equations of straight pipes with local wall-thinning defects under single and complex loads were fitted. Based on the allowable load on the equipment nozzles, the influences of torque and axial force on the load-bearing capacity of straight pipes with local wall-thinning defects were quantitatively analyzed. For medium and low-pressure equipment, the load-bearing capacity was reduced by 0.59~1.44% under the influence of torque, and by 0.83~1.80% under the influence of axial force. For high-pressure equipment, the load-bearing capacity was reduced by 10.07~20.90% under the influence of torque, and by 2.01~12.40% under the influence of axial force.

Active nonlinear vibration control of a membrane solar array structure

Membrane solar array has attracted a lot of attentions in recent years because of the advantage of light-weight, low-cost, and high-folding-ratio. Meanwhile, the membrane solar array structure also pose challenging large-amplitude vibration issue which will impact the performance of the spacecraft significantly. In this paper, active nonlinear vibration control of a membrane solar array structure is studied. Based on the nonlinear finite element method, a nonlinear dynamic model of the structure is established. The optimal positions of piezoelectric actuators are determined by optimizing a controllability optimization criterion with Particle Swarm Optimizer algorithm. An active controller is designed to suppress the undesired nonlinear vibration based on the linearized dynamic model by using the LQR control method. Simulation results show that the designed active controller can suppress the nonlinear vibration of the membrane solar array structure effectively, and the optimally placed actuators can produce better control effect with smaller control inputs.

Numerical simulation of fragment impacting solid rocket motors

For the initiation characteristics of solid rocket motors (SRMs) filled with high-energy solid propellant under fragment impact, the related theoretical critical criterion for shock initiation was established based on the critical energy criterion and equivalent analysis method. Afterward, numerical simulation of fragment impacting SRM was carried out by using the ANSYS/LS-DYNA software and the nonlinear finite element method. Based on the calculated pressure and reactivity in the high-energy solid propellant grain, the shock critical initiation velocity of SRM and its variation with different forms of fragments and impact conditions were determined. It is found that the numerical simulation results under typical conditions are in good agreement with the data calculated with the developed theoretical critical criterion for shock initiation of SRM. However, the shock initiation mechanism becomes more complex when the case thickness of SRM increases to more than 5 mm; thus, the applicability of the developed theoretical critical criterion reduces. Moreover, it is found that all the case thickness, fragment shape, material properties of the fragment, and impact attitude can significantly affect the shock critical initiation velocity of SRM, even the initiation position and time. First, the critical velocity increases linearly with the increase in case thickness, and the increment rate is faster beyond the thickness of 6 mm. Second, the shock critical initiation velocity induced by fragments with different shapes is as follows: spherical fragment > cubic fragment > cylindrical fragment, while the initiation capacity of different fragment materials is ranked as follows: tungsten alloy > 45 steel > 2024 aluminum. Third, the effects of impact attitude on the shock critical initiation velocity, position and time are complex, and these effects are also influenced by fragment shape. When the impact angle is less than 60°, there is a higher shock critical initiation velocity of SRM under inclined impact than that under positive impact. In addition, the critical velocity induced by cubic fragment is the highest under the combination of vertex impact and positive impact. The variation of the critical velocity under this condition is approximately consistent with that by impacting with cylindrical fragment. Furthermore, when the impact angle is greater than 60°, the shock critical initiation velocity of SRM is less obviously influenced by impact attitude and fragment shape. Meanwhile, the critical velocity decreases sharply under this condition, which indicates that it is easier for SRM to detonate.

Ultimate Strength Analysis of Roro Passenger Ship under Combined Global and Local Load Using Nonlinear Finite Element Method

Since roro passenger ships have specific characteristics in handling cargo with the roll-on-roll-off loading and unloading system that must be equipped with a ramp door. Therefore, it is important to conduct the ultimate strength analysis by considering local loads and global loads to ensure the level of safety and reliability of the ship structure. The aim of this research is focused on the investigation of the structural response and the ultimate strength of the roro passenger ship using the non-linear finite element method. The dynamic explicit method is conducted to estimate the large displacement of the deformed structures such as the hull girders, deck girders and plates. In the structural response analysis, the results shows that maximum stress was occurred on the deck girders due to the sagging bending moment load. In the ultimate strength analysis, it is identified that hydrostatic load have reduced the ultimate strength about 33 %. Otherwise, the ultimate strength is increased about 1 %, in the sagging condition.
 HIGHLIGHTS
 
 The nonlinear behavior of the roro passenger ship ultimate strength due to the combined global and local load is presented
 On the hogging condition, the addition of local load (hydrostatic pressure) reduce the roro ship ultimate strength about 33 % compare to the pure global ultimate bending load
 On the sagging condition, the hydrostatic pressure have slightly increased the ultimate strength around 1 %
 
 GRAPHICAL ABSTRACT

The dynamic ultimate strength of stiffened panels under axial impact loading

ABSTRACT The dynamic ultimate compressive strength of stiffened panels under longitudinal compressive impact is studied based on the non-linear finite element method (FEM), and an empirical formula was derived based on the results. Three types of initial deflections are considered in numerical simulation. The FE procedure was validated by comparing with existing formulas and published pieces of literature. The influences of parameters, such as material yield stress, impact duration, impact shape, plate thickness ratio, plate aspect ratio, web height ratio and web thickness ratio, were investigated. The results indicate the impact duration has a significant influence on the non-dimensional dynamic ultimate strength; the geometrical parameters and material yield strength also have a certain effect. While with the same duration, amplitude and impulse, different impact shapes have little influence. The fitting accuracy of the formula was proved by a comparison between the proposed formula and FE results. And its applicability was validated by applying to real ship panels.

Analysis of mechanical properties of steel-concrete joint of large-span hybrid beam bridge

The mechanical properties of the steel-concrete joint determine the mechanical properties of the whole bridge. The mechanical properties of the steel-concrete joint of Jianhua railway rigid-frame bridge are analyzed by using nonlinear finite element method. The results show that the overall stiffness transition of the joint is smooth, the maximum stress of concrete section and steel box girder section are lower than the design value of the strength, which indicates that the structural stiffness and strength of the steel-concrete joint section meets the requirements. The error range of the finite element analysis results and the measured data is within 6 %, which shows that the finite element method can simulate the actual stress state of the bridge and it could save a lot of time and energy compared to the actual test.

Numerical study on buckling of aluminum extruded panels considering welding effects

Aluminum extruded panels are increasingly used in marine structures as lightweight solutions. Less welding is needed for such extrusions than traditional built-up panels of welding stiffener to plate sheets. However, the buckling mode and ultimate strength of aluminum extruded panels are difficult to predict with existing formulas due to different welding sensitivity. This paper presents a numerical study on the buckling of aluminum extruded panels, with the effects of welding taken into account. The numerical study was done with the nonlinear finite element method. The simulations were verified by comparing them with experimental results from the literature. The sensitivity of the ultimate load with respect to the welding effects was determined by parametric studies. The effect of inertia forces on the stiffener-tripping buckling mode was investigated. The influence of the slenderness ratio on the heat-affected zone (HAZ) effects was analyzed. The simulations can be also used as a foundation for developing improved analytical formulations.

Transient planar dynamics of cable-payload systems using geometrically exact beam theory

We investigate the planar dynamics of aerial payload systems, in which we model the tow-cable as a geometrically exact (GE) beam and the payload as a rigid body. A GE beam incorporates large displacements, large rotations, and cross-sectional shear. Aerodynamic loads on the cable are computed on each element and then summed. Given its large mass, the towing aircraft is taken to be unaffected by the system’s motion. We derive the equations of the system and solve these using a nonlinear finite element method. We then study the effect on the system’s dynamics of cable length, payload size, downwash, and wind speed. Finally, we investigate practically relevant transient flight scenarios. We find that the flight path influences the system’s response, and minimizing motion derivatives limits payload’s motion. Our general formulation is easily extended to three-dimensions and useful for many aerial or underwater towed systems.

Finite element analysis of pitting corrosion on mechanical behavior of E690 steel panel

PurposeThe purpose of this study is to analysis the pitting corrosion on the mechanical behavior of E690 high-strength steel sandwich panel. The pitting corrosion depth and degree of pitting (DOP) damage were used to evaluate the mechanical behaviors such as peak load and specific energy absorption of E690 panel.Design/methodology/approachThe mechanical behavior of quasi-static compression, low-speed impact and three-point bending of E690 panel after pitting corrosion was simulated by ABAQUS nonlinear finite element method.FindingsThe quasi-static compression and low-speed impact mechanical properties can be greatly reduced by the pitting corrosion of the panel core, the pitting corrosion of the outer panel shows no obvious effect. The mechanical properties decrease with the increase of the pitting corrosion depth and DOP, and the influence of DOP is greater than that of pitting corrosion depth. The DOP of outer panel has less effect on mechanical properties of three-point bending compared with that of the core. Therefore, the pitting corrosion in the core of panel should be strictly controlled to prevent adverse effects on the mechanical properties of the structure.Originality/valueTo make up for the deficiency of the research on the corrosion behavior of high-strength steel sandwich panel structure, this paper chose E690 high-strength steel panel as the research object, and nonlinear finite element method was adopted to simulate the influence of pitting corrosion coverage area and pitting depth on its mechanical property degradation. The quasi-static compression, low-speed impact and three-point bending mechanical properties of panel with various DOPs and pitting depths were systematic studied.

An empirical formula to assess ultimate strength of initially deflected plate: Part 1 = propose the general shape and application to longitudinal compression

This study proposes a simplified empirical formulation to predict the ultimate strength of the initially deflected plate subjected to longitudinal compression. The empirical formulation's applicability and accuracy were verified by comparing the nonlinear finite element method (NLFEM). In total, 700 cases of initially deflected plate scenarios by assuming the buckling mode shape were adopted as the input data. For the simplification of the plate design process, a general shape of the empirical formula is proposed based on input data. A reliable technical solution is obtained with good agreements (R2 = 0.98 to 0.99) compared to NLFEM. The advantage of the proposed outcome is documented by comparing the previous study. The obtained result could be beneficial for the structural design of the initially deflected plate in predicting its ultimate strength performance under longitudinal compression.

Numerical and theoretical analysis of beam-to-column connections with ECC ring beams subjected to local compression loading

Engineered cementitious composite (ECC) is a kind of high performance cement-based composite materials with strain hardening and multiple cracking behaviour. Replacing concrete with ECC in the beam-to-column connection with ring beam may effectively improve the load-carrying capacity and ductility, as well as prevent cracks and solve durability problems caused by the brittleness of concrete. In this paper, the failure mechanism of beam-to-column connection with ECC ring beam subjected to local compression loading was investigated with the nonlinear finite element (FE) method. The results indicated that continuous lateral pressure was provided by the ECC ring beam, which improved the local compression performance of the ring beam connection. Extensive parametric studies on the local compression behavior of connections with ECC ring beams were also conducted. According to the simulation results, the peak strength of ECC connections was 13.0%–24.2% higher than that of concrete specimens. Increasing the ECC compression strength or ring beam width can effectively increase the load-carrying capacity of the connection, but the ECC tensile strain can only affect the ductility of the connection when the ultimate tensile strain was lower than 1.5%. Based on the FE analysis, an effective restraint width of the ECC ring beam was proposed, and theoretical models were established to predict the axial compressive bearing capacity of the beam-to-column connection with ECC ring beam.

Axial Compressive Buckling of a Double-Limb Column in a Precipitator Casing

In the side supporting structure of a precipitator casing, the skeleton column is sometimes designed as a composite section composed of double H-shaped steel limbs and connecting wallboard. Column buckling is characterized by its special section and the stressed skin effect from wallboard. The influence of initial imperfections and structural parameters on column stability was investigated using the nonlinear finite element method. The residual stress has a slight adverse effect on column stability. The buckling modes can be categorized into two types: 1) buckling of connecting wallboard; 2) simultaneous buckling of connecting wallboard and flexural-torsional buckling of H-shaped limbs in top segment. Column stability significantly increases with increasing connecting wallboard thickness, decreasing connecting wallboard width, and decreasing distance between the connecting wallboard and the rear flange of H-shaped limbs. The structural parameters of the wallboard, angle steel stiffeners, and transverse brace interval have no noticeable effect. Column stability slightly increases with a decrease in the width-to-thickness ratio of flange, the height-to-thickness ratio of web, and torsional slenderness ratio. Based on the simulation results, a buckling capacity calculation recommendation was developed for an axial compressive double-limb column, which is important for the design of heavily stressed double-limb columns in box-type structures.

Dynamic reliability evaluation of buried corroded pipeline under rockfall impact

Load impact, such as the rockfall, may bring significant threats to the integrity management of pipeline. This study is intended to evaluate the reliability of buried pipeline under rockfall impact, and so as to reduce the possible failure and unnecessary downtime. Firstly, the dynamic response of the buried pipeline under load is analyzed by Euler Bernoulli foundation beam. After that, the process of rockfall impact on buried corroded pipeline is simulated with nonlinear finite element method. Furthermore, the influence of rockfall’s parameters (including rockfall mass, impact velocity, impact position, etc.) on the pipeline’s equivalent stress is quantitatively analyzed. Eventually, a time-varying reliability model is established to calculate the failure probability. The results indicate that the mass and velocity of the rockfall have obvious influence on the pipeline’s failure probability, and the change of impact’s position has small influence. The proposed method can provide a theoretical reference for the design and maintenance of buried pipeline.