Gap Elements Research Articles

A discrete nonlocal damage mechanics approach

In this paper the authors develop the governing equations for a finite element model of micro-cracking based on a novel approach, eschewing differential equations and continuum mechanics. Instead of first stating the continuum balance laws and constitutive relations followed by discretization, the body is discretized first and then the equations of equilibrium are directly stated for the discretized body. It is shown that, as a result, the balance laws and constitutive relations can be entirely stated in terms of edge forces and lengths rather than strains. Furthermore, by ensuring that microcracks always propagate along the dual mesh which represents the possible fracture microplanes in the element, the need for creating additional nodes, gap elements or cohesive zones is avoided. Finally, the notion of the survival probability of a fracture microplane is introduced and the transition probability evolution is described by using probabilistic notions from population models. Thus the resulting governing equations can be solved by a conventional elastic predictor, followed by a nonlocal fracture corrector, making this convenient to augment conventional elements with fracture abilities.

Comparison of Interstorey Drift in General RC Buildings in Pounding and No Pounding Case

Inter-storey drift is an important parameter of structural behavior in seismic analysis of buildings. Pounding effect in building simply means collision between adjacent buildings due to earthquake load caused by out of phase vibration of adjacent buildings. There is variation in inter-storey drift of adjacent buildings during pounding case and no pounding case.
 The main objective of this research was to compare the inter-storey drift of general adjacent RC buildings in pounding and no pounding case. For this study two adjacent RC buildings having same number of stories have been considered. For pounding case analysis there is no gap in between adjacent buildings and for no pounding case analysis there is sufficient distance between adjacent buildings.
 The model consists of adjacent buildings having 4 and 4 stories but unequal storey height. Both the buildings have same material & sectional properties. Fast non-linear time history analysis was performed by using El-centro earthquake data as ground motion. Adjacent buildings having different overall height were modelled in SAP 2000 v 15 using gap element for pounding case. Finally, analysis was done and inter-storey drift was compared. It was found that in higher building inter-storey drift is greater in no pounding case than in pounding case but in adjacent lower height building the result was reversed. Additionally, it was found that in general residential RC buildings maximum inter-storey drift occurs in 2nd floor.

Seismic performance assessment of multi-story RC buildings with soft-story collapse mechanism equipped with gapped inclined bracing (GIB)

Gapped inclined bracing (GIB) is an innovative retrofit system for buildings with soft-story collapse mechanism. The system consists of a brace with gap element that activates before the structure approaches post-capping negative stiffness and collapse, providing supplemental plastic deformation and enhancing ductility of the system. This technique is also a resilient solution as the damage is controlled at the retrofitted soft-story, reducing the cost and time of repair. The paper presents a numerical study to verify the application of GIB systems for modern RC buildings, where masonry infill panels may be removed from lower stories due to functional requirements for more open spaces. Based on nonlinear static analysis, a novel and efficient design method is proposed to determine the GIB design parameters. To verify the performance of the retrofitting methodology, 12 configurations of RC moment frames with 4 and 8 stories are designed according to modern seismic codes and subjected to nonlinear static and incremental dynamic analyses. The results are then used to conduct fragility analysis to assess classical performance levels including immediate occupancy, life-safety, and collapse prevention. The results show that using the proposed design of GIB elements, the ultimate drift capacity corresponding to the collapse of soft-structures are increased by a factor of two. Also, the probability of collapse is reduced by 50% increase in the median collapse hazard intensity. These highlight significant improvements in the safety and resilience of buildings with soft-stories.

DYNAMIC ANALYSIS OF COMPOSITE MULTI I-GIRDERS BRIDGE USING FINITE ELEMENT METHOD

Three dimensional finite element models are developed to deal with the bridge-vehicle interaction problem of simply supported composite multi I-girders bridge. The bridge is modeled by using ANSYS 15.0 program with solid and shell elements to represent concrete and steel members, respectively. AASHTO HL-93 truck is idealized as 3D non-linear model consisting of five lumped masses connected by rigid beams and supported by spring-dampers. The separation between the tires and road surface and surface roughness condition are simulated by Gap and actuator elements, respectively. The road surface roughness profiles are generated from power spectral density (PSD) and cross spectral functions. The models used are capable to take all bridge and vehicle responses into consideration with no limitations on the complexity of the models. The dynamic responses of the multi I-girder bridge are investigated under conditions of various loading positions, roughness classes, vehicle speeds, and bump height. The dynamic behaviors are presented in terms of Dynamic Amplification Factors (DAF). The results show the girder that itself supporting the moving vehicle has lower value of DAF because of higher static responses. A 45 km/hr vehicle speed provides higher DAF value. The bump heights have significant effect on DAFs for bridge with short span.

New electromagnetic band gap antenna for multiple ultra wide band applications

This paper presents a compact multiband microstrip electromagnetic band gap (EBG) patch antenna with partial ground used for the 2nd and 3rd mode excitation, allowing multiple band resonance and control of the resonance frequencies. The electromagnetic band gap elements are inserted to improve obviously output parameters (gain directivity, return loss, maximum radiation Intensity, and radiation efficiency). Simulation and measurement results show a multiband antenna WiMAX, WLAN-band applications that can effectively cover three separated bandwidths (2.12, 3.1 and 5.41 GHz). The proposed compact antenna is grounded on a 1.6 mm-thick FR4 epoxy substrate with overall dimension of 0.305λ × 0.305λ × 0.012λ at lower frequency. The whole size of the proposed antenna with an overall area of 25 × 38 × 1.6 mm3 is maintained, and a low cross-polarization level within the operating frequency range. Electromagnetic Band Gap materials, artificially engineered structures, have the main role to improve the output performance of the patch antennas.

Reduction of Mutual Coupling in Compact Antenna Array Using Meander Line Slot EBG Structure

This paper presents the design and the fabrication of a compact Multiple-Input Multiple-Output (MIMO) antenna array with very low mutual coupling, operating in the 2.4 GHz band. The compact design is achieved by the introduction of a meander line structure in the conventional patch antenna. The reduced mutual coupling of about 52 dB is realized by inserting a periodic array of Electromagnetic Band Gap (EBG) elements in the radiating antenna elements. A prototype of the proposed antenna array has been manufactured on an FR4 substrate with a dielectric constant of 4.4 and a height of 1.6 mm. The excellent agreement between simulated and measured data confirms the performance of the proposed antenna array in a MIMO environment. This MIMO antenna array has a compact size of 0.40λ0×0.2λ0. For the validation of the results, the overall dimensions and the isolation level of the proposed design have been compared with designs previously reported in the literature and it has been found out that the proposed design is superior in both isolation level and compactness than its counterparts.

Time-domain Spectral Finite Element Method for Wave Propagation Analysis in Structures with Breathing Cracks

Guided waves are generally considered as a powerful approach for crack detection in structures, which are commonly investigated using the finite element method (FEM). However, the traditional FEM has many disadvantages in solving wave propagation due to the strict requirement of mesh density. To tackle this issue, this paper proposes an efficient time-domain spectral finite element method (SFEM) to analyze wave propagation in cracked structures, in which the breathing crack is modeled by defining the spectral gap element. Moreover, novel orthogonal polynomials and Gauss–Lobatto–Legendre quadrature rules are adopted to construct the spectral element. Meanwhile, a separable hard contact is utilized to simulate the breathing behavior. Finally, a comparison of the numerical results between the FEM and the SFEM is conducted to demonstrate the high efficiency and accuracy of the proposed method. Based on the developed SFEM, the nonlinear features of waves and influence of the incident mode are also studied in detail, which provides a helpful guide for a physical understanding of the wave propagation behavior in structures with breathing cracks.

Preparation and Properties of Spherical Mo Powders by Plasma Rotating Electrode Process for Additive Manufacturing

Since molybdenum has very high melting point of 2620 °C, there are many difficulties in its forming and post-processing, especially for deep processing. Furthermore as molybdenum is expensive, the utilization rate is important for the molybdenum processing. Additive manufacturing can directly manufacture the parts without mold and increase the utilization rate, and brings an opportunities for the new direction of deep processing for molybdenum. Due to the high quality requirements of molybdenum powder in additive manufacturing technology, the high-quality spherical molybdenum powder was prepared by plasma rotating electrode process method in the present study. The morphology, particle size and particle size distribution, chemical and physical properties were investigated. The molybdenum powder prepared by plasma rotating electrode process method showed to have high purity, high sphericity, good fluidity and high bulk density, proper particle size distribution and low gap element within the powder. The microstructure of the powder was a mixed structure of dendrites and cell crystals formed by rapid solidification, and as the particle size of the powder gradually decreased, the microstructure of the powder surface was remarkably refined. Within a certain range, the molybdenum powder with a wide particle size distribution had better fluidity and higher bulk density. The high-quality spherical molybdenum powder was prepared by plasma rotating electrode process method, which can meet the requirements of additive manufacturing technology for powder material performance.

Post-buckling transition of compressed pipe strings in horizontal wellbores

In offshore oil and gas wells, the post-buckling transition of compressed pipe strings is a significant engineering problem to be addressed, particularly in horizontal wellbores. Many hypotheses exist in theoretical research, and it remains difficult to accurately measure the post-buckling mode in experimental tests. In the current study, the compressed pipe strings initially located at the bottom of horizontal wellbores were discretized into beam elements, and a gap element was introduced to detect the contact between the horizontal strings and the wellbores. The dynamic relaxation algorithm was used in finite element analysis to improve the weak points of the theoretical and experimental research. The calculation results show that the post-buckling transition exhibits nonlinearity. Based on the calculated post-buckling modes, the dimensionless critical loads for sinusoidal and helical buckling were identified. After sinusoidal buckling, it was observed that the compressed string was not in continuous contact with the horizontal wellbore, and two non-contact sections appeared near the string ends. These numerical results are beneficial for understanding the post-buckling behaviors of horizontal strings in wellbores.

Photoluminescence and photocatalytic hydrogen evolution properties of orange-red emitting AlN:Sm3+

Sm3+ ions doped orange-red emitting AlN phosphors were successfully fabricated by a simple solid-state route at 880 °C. The phase analysis and crystal structure, symmetry, morphology, band gap width, elements analysis and photoluminescence properties are investigated detailly. The symmetry of the local environment for Sm3+ depends on the doping concentration of Sm3+ ions in AlN matrix. All the phosphors can exhibit orange-red emission by virtue of the 4G5/2 → 6H7/2 transition of Sm3+ ions. And all the phosphors display high color purity and low correlated color temperature. The best doping concentration of Sm3+ in AlN matrix is 1.0% mole fraction. Furthermore, in contrast to undoped AlN, AlN:xSm3+ semiconductors show excellent photocatalytic hydrogen evolution activity, and the maximum rate of H2 evolution from water splitting is 98 μmol h−1 g−1 when the doping concentration of Sm3+ is 1.3% mole fraction. The study signifys bifunctional AlN:xSm3+ with luminescence and photocatalytic properties may be anticipated to apply in both white light-emitting diodes (WLEDs) and photocatalytic hydrogen evolution from water splitting.

The Effect of Mass, Depth, and Properties of the Soil Below the Raft Foundation on the Seismic Performance of R.C. Plane Frames

Soil structure interaction has been the subject of numerous studies. The foundation soil has a definite effect on the performance of structures during seismic excitation. Recent studies show that the effect of soil-structure interaction SSI may be detrimental to the structure during seismic excitation. In this study, the effect of consideration of the soil below foundation and its depth, and the soil modulus of elasticity on the response of structures is investigated. The number of mode shapes considered has an effect on the accuracy of the values of structure response. A structural model consisting of an 8-story reinforced concrete frame resting on raft foundation, and including the soil below the raft is analyzed. The frame is analyzed using SAP2000 software, and time history and modal analysis are carried out with varying values of both soil depth and soil modulus of elasticity. The soil below the foundation is connected to the raft elements by gap links. Gap element links are compression–only members with appropriate stiffness, which are active only in compression. Modal analysis results show that the periods of vibration decrease as the modulus of elasticity of the soil increases. Periods of vibration of the frame without the soil mass consideration are less than those when the soil mass below the raft is considered, and they increase with increased depth of foundation to a certain limit. The structures response in the form of columns shear forces and story displacements are also evaluated under the variable parameters considered.

Seismic performance analysis of multi-story RC frames strengthened with RC infill wall

Seismic performance of RC frame structures was investigated by creating 3-D models of the frame with additional solid RC infill wall along the height of Honolulu Building prescribed in FEMA design examples. Layered-shell element (LSE) was used to model the infill wall and gap element was introduced at the interface between the wall and the bounding frames. The modelling technique was validated against test results reported in the literature prior to its application on the 12 story building. The push over curves of all models were compared to obtain the most efficient model that conform to the strength and stiffness requirement of the seismic codes of Indonesia. The results showed that the non-linear behaviour of RC frame with RC infill wall can be modelled accurately using LSE and gap element. The RC wall addition improved the strength, stiffness and performance of the frame significantly. The most efficient model was that with infill wall up to the first 4 story levels in which, the performance of the structure improved from collapse prevention to immediate occupancy.

On the post-buckling analysis of a circular column with cylindrical constraint under concentrated torque loading

With the hypotheses of small deformation and Bernoulli-Euler beam, a gap element is introduced to describe the contact between the circular column and the external cylinder. The dynamic relaxation method is used to calculate the static equilibrium of the twisted column constrained by the cylinder. The post-buckling modes of a torsional column in a cylinder are investigated for the deformation configurations of one-point, two-point, three-point, and point-line-point contact. It is found that the end constraint has an effect on the length of the two suspended sections of helical buckling mode, but has no effect on the length of the continuous contact section in the middle. The relations have been derived among critical torque, post-buckling modes, lengths of each section, and loads (including shear, bending moment, and contact force). Finally, the torsional buckling has been investigated for sucker rods and drill pipes with lengths of 1 km. It is found that the helical buckling of multiple pitches occurs. The results of the current study provide theoretical guidance for the design of centralizer spacing in oil and gas engineering applications.

Study and Analysis of Pounding Effect between Adjacent RC Buildings

Pounding occurs when the adjacent buildings start vibration out of phase during the seismic activity which causes the collision between the adjacent structures. Due to higher cost of land in cities people have tendency to attach the buildings at property line. Earthquakes can cause pounding when adjacent buildings have little gap or no gap providing separation. Due to pounding effect structural and non – structural damage may occur in the adjacent buildings.
 The main objective of this research is to assess the seismic response of common residential RC buildings that has been constructed with no gap with the adjacent structures and to find the minimum gap requirement for the commonly constructed buildings of Nepal.
 For this study two different cases with varying separation distance between adjacent buildings have been considered. First case is the adjacent buildings having equal storey height but different number of stories. It includes models having 4 and 2 stories and 4 and 3 stories. Second case is the adjacent buildings having unequal storey height but same number of stories. It includes models having 3 and 3 stories and 4 and 4 stories. In both cases adjacent buildings have same material & sectional properties. Non-linear dynamic analysis is performed using El-centro earthquake data as ground motion. Gap element has been used to simulate the pounding force between buildings. Adjacent buildings having different overall height are modelled in SAP 2000 v 15 using gap element for pounding study. The seismic responses in terms of joint displacement, joint acceleration, pounding force are presented. Joint displacement and joint acceleration comparison for both pounding and no pounding cases are presented.
 Gap calculation from NBC and IS code, ABS and SRSS method was compared with gap required to avoid pounding force between adjacent structures and appropriate gap was recommended.

A Novel Gap Element for the Coupling of Incompatible Interface in Component Mode Synthesis Method

The component mode synthesis (CMS) methods are often utilized for modal analysis to investigate the vibration characteristics of the complex structures which are commonly divided into several substructures. However, non-matching finite element meshes may occur at the interfaces between components and virtual gaps are easily produced along the curved interfaces, which limit the application of CMS and lead to larger numerical errors for vibration analysis. To overcome the problem, a novel gap element method (GEM) is employed into a free-interface CMS method in this paper, where both displacements and forces of the nodes on the incompatible interfaces are introduced by two independent Lagrange multipliers to enforce the compatibility conditions. Two-dimensional numerical examples are given to validate the effectiveness of the proposed method. The results of natural frequencies and modal shapes obtained using the proposed method agree very well with the ones obtained using full finite elements model, no matter the gaps along the interface exist or not. The influence of the number of nodes on the non-matching interfaces on the accuracy of frequencies is also discussed.

Post-buckling analysis of compressed rods in cylinders by using dynamic relaxation method

Buckling of rods with cylindrical constraints is an essential problem in engineering and medical fields. Completely different to the buckling of classical Euler rods, the post-buckling modes for rods with cylindrical constraints involve highly complicated deformations and geometric configurations. In this paper, the rods are discretized into beam elements by finite element method, and the constraint relation between the rods and cylinders is described by gap element. A dynamic relaxation method for static buckling of compressed rods in cylinders is introduced. Numerical simulations have been carried out to investigate the effects of damping, element length, initial contact stiffness and penetration on post-buckling, etc. The characteristic buckling modes include deflection curves with single point, two points, three points and point-line-point contact. For the helical buckling, it is found that the transition section consists of two noncontact sections only, while the perturbed-helix section does not exist. Except the critical load and shear force of helical buckling, numerical simulation results are in good agreement with the analytical solution. By using the dynamic relaxation method, stable helical buckling modes can be obtained directly without undergoing sinusoidal buckling deformation under given compressive loads.

Effects of Boundary Condition Models on the Seismic Responses of a Container Crane

In recent years, several large earthquakes have caused the collapse of container cranes, which have resulted in halting of freighting, and significantly affected the economy. Some reports are concerned the uplift and derailment events of crane legs, and the collapse of the crane itself. In this study, the effects of different boundary conditions used in the numerical method are investigated for a container crane under seismic excitation. Three different boundary conditions are considered in terms of the connection of the crane’s legs (wheels) and the ground (rails), namely pin support (PIN), gap element (GAP), and Friction contact (FC) elements, by using the SAP2000 program for a typical container crane. Then, time history dynamic analyses are conducted using nine recorded ground motions. Dynamic behaviors of the container crane are studied in terms of the total base shear, portal drift, and relative displacement of legs, by investigating the three types of base boundary conditions. The results of the study show that when the intensity of earthquakes is large enough to create uplift and derailment events, the selection of the boundary condition model considerably affects the dynamic responses of the container crane. In addition, when uplift and derailment of the crane occur, the FC support condition is the most compatible with the real behavior of the crane. On the other hand, under low seismic excitation, there is no significant difference of the crane behavior according to the choice of boundary condition model.

Скінченноелементний аналіз пружно-пластичного стану тріщини на межі розділу площини з круговим включенням

The problem on determining of elastic-plastic stress-strain state of infinite plane with a circular inclusion made from another material and an arc crack at the interface under action of arbitrary mechanical loadings applied at infinity is considered using the FEM approach. The problem is resolved within the framework of contact model for which the possibility of appearance of contact macrozones between crack faces is assumed. The isotropic hardening of materials with bilinear approximation of stress-strain curves is considered. The infinite plane is modeled by square domain whose size is of an order of magnitude greater than inclusion diameter. Contact interaction of crack faces is simulated using gap elements. To obtain the energy release rate the J-integrals are calculated along several closed contours around the crack tips. The comparison of obtained results with available analytical solutions for linear elasticity shows that insignificant differences take place during transformation from pure elastic to elastic-plastic stress-strain state.

Virtual tetrahedral gap element to connect three-dimensional non-coincident interfaces

This study introduces a new version of a virtual tetrahedral gap element to connect partitioned structures which are independently discretized with tetrahedral elements. Tetrahedral meshes are widely used for practical engineering problems due to their simplicity. The proposed interface method employs the localized Lagrange multiplier method. The virtual tetrahedral gap elements are placed between the frame-slave and frame-master interfaces. The surface of the tetrahedral meshes is triangular; thus, a virtual tetrahedral gap element is developed. A distinct feature of the virtual tetrahedral gap element is that it has a zero-strain condition which provides the exact interface reaction forces at the non-matched interface. The proposed tetrahedral gap element handles three-dimensional interface problems more effectively than conventional segment-to-segment methods. It also provides better accuracy. The validity and robustness of the proposed method are demonstrated by several numerical examples.

A Visualization Technique to Predict Abnormal Channeling Phenomena in the Blast Furnace Operation

An uneven gas distribution through the burden layers inside a blast furnace (BF) results in abnormal gas resistance or pressure changes. Rapid variations in the abnormal gas resistance will lead to the occurrence of channeling. A visualization technology mainly made of pressure distribution was developed to predict BF channeling phenomena in this study. The real-time data of BF shaft pressure was used to create a 3D visual model by neural network algorithms and 3D real-time BF pressure changes were observed. The root mean square deviation (RMSD) of the BF shaft pressure was used as an index to set up the predicting criteria of channeling occurrence with the opening of BF Annular Gap Element (AGE), and a predicting system based on the criteria was built. The two criteria for the channeling alarm are the RMSD of the BF shaft pressure (> 0.15 kg/cm2) at the upper two levels, and the AGE opening being greater than 60%. This system has been installed in the China Steel Corporation (CSC) BFs, and the test results showed that a prediction can be obtained 8 to 16 min ahead of channeling allowing sufficient time for the operator to adjust the BF operation in order to avoid the occurrence of channeling.