Adaptively Shifted Integration Research Articles

An integrated finite element analysis and virtual reality system for structural and indoor nonstructural components of buildings under seismic excitations

Nonstructural components such as furniture, ceilings, and lighting equipment exhibit varying behaviors during earthquakes influenced by factors such as seismic waves, floor heights, friction coefficients of floors, and the proximity of other objects. These variables can differ in each scenario, rendering it challenging for individuals to understand and implement effective seismic protection measures for these components. Under these circumstances, this study aims to develop an integrated finite element analysis and virtual reality (VR) system to simulate and visualize the behavior of indoor nonstructural components under seismic excitation. The finite element analysis system was developed using an adaptively shifted integration (ASI)–Gauss code, and the VR system was implemented using Unity software. For the analysis, the models of the furniture and ceilings were placed on the 1st, 5th, and 10th floors of a 10-story reinforced concrete building model. The seismic response was analyzed using the 100% 1995 JMA-Kobe seismic wave as the input. The results indicated that the 10th floor experienced the most severe damage, with complete ceiling collapse and furniture overturning. On the 5th floor, the ceiling underwent significant plastic deformation without collapsing, and the furniture moved and swayed but remained upright. On the 1st floor, the furniture also moved and swayed, with one piece toppling over. These findings highlight the variability in damage across different floors. Finally, this damage was realistically visualized using VR goggles, which could serve as a powerful tool to enhance public awareness of disaster prevention and mitigation.

Numerical investigation on mechanical behavior of door systems during seismic excitation

The opening and closing of doors in buildings likely become challenging when earthquakes occur owing to the deformation of the door frames. Although this may delay evacuation, there are no anti-seismic standards for doors defined in the Japanese Building Standards Act, which was amended in 1981. Discussions on doors or door frames from a structural point of view are still rare, even though the behaviors of doors, door frames, and hinges under seismic excitation are critical for avoiding secondary disasters after earthquakes. In this study, a seismic response analysis of a building model with door frames was performed using the adaptively shifted integration (ASI)-Gauss code to find an approach to reduce the deformation of door frames. Numerical results confirmed that the severe damage to the non-structural wall caused by the interlayer deformation of the building allowed both door frames and doors to be severely deformed. The in-plane deformation angles exceeded the angles causing difficulty in opening the doors. A door acted as an element resisting the door frame from deforming on the upper floors, and the door function would be lost on the lower floors by deforming in the out-of-plane direction. Furthermore, the overall deformations of the door frames decreased significantly even on the lower floors, where the interlayer drift angle of the building was larger, by placing the door system in a setback position. This effect was greater when the setback length was longer.

Explosive demolition planning of building structures using key element index

A systematic and appropriate selection of columns to be removed should be conducted to ensure the safe and reliable demolition of old or uninhabitable buildings. However, the explosive demolition techniques used at present mostly rely on experiences and know-how built up by predecessors and are not fully open to general users. Therefore, a clear selection criterion for columns to be removed should be developed based on a quantitative value that indicates the contribution of each column in a building structure. This study applied a key element index to evaluate the contribution of columns and their variance to multistage explosive demolition planning. An adaptively shifted integration (ASI)-Gauss code was used to simulate and investigate the explosive demolition sequences of a 10-story steel-framed building. Various timings between the multistage blasts were evaluated by comparing the efficiencies and levels of safety during demolition. By removing the groups of columns from those that had a greater influence on the variance of the key element index values, a large difference was obtained in the distribution of the index values, especially in the lower structure. The results showed that if a building is not too weakened in the initial blast, the 2nd blast of the main blasts should be conducted at the moment of impact between the upper and lower structures or the following short time to make the most of the impact. The results also showed that too much weakening of a building at the preceding stage might not provide full advantage of the impact that occurs between the main blasts.

Numerical Investigation on the Collapse of the ChamplainTowers South in Florida

In this study, the building collapse of the Champlain Towers South in Florida allegedly caused by deck collapse was examined through the finite element analysis based on the existing hypotheses and investigation. For the numerical analysis, the Adaptively Shifted Integration (ASI) – Gauss code was applied. In addition, the member strength failure algorithm of RC components was modified and the flat-plate structure was introduced into the numerical model of the building. According to the numerical results, the building did not collapse when the external deck of the building connecting the columns, so called as key elements, were removed by the collapse of the external deck.

Sequential Simulations of Steel Frame Buildings Under Multi-Phase Hazardous Loads During Earthquake and Tsunami

Based on the experience of the 2011 Great East Japan Earthquake and the following tsunami, this study aims to develop effective analytical tools that can comprehensively be applied to buildings under multi-phase hazardous loads such as seismic motion, fluid force, and debris impact. Simulations by two kinds of analytical tools were conducted. First, a structural collapse analysis of a steel frame building under successive applications of varying loads was performed using the ASI (Adaptively Shifted Integration)-Gauss code, which simulates behaviors of structures by simple modeling. The steel frame building model was first excited under an acceleration record observed in Kesennuma-shi during the earthquake, and fluid forces due to a tsunami wave were applied. Then, the collapse behavior of the building was investigated by implementing a sophisticated contact algorithm in the numerical code to express a collision between debris and a building. It became evident that the damage to the building intensifies if a head-on collision occurs under a tsunami flow with a lower inundation height, and the damage to the building becomes larger if sideway collisions occur under a tsunami flow with a higher inundation height and higher velocity. The second simulation was conducted by using the stabilized finite element method based on the volume of fluid method, to estimate a drag coefficient of an actual tsunami evacuation building with openings. The practicability of an estimated wave force using the drag coefficient was confirmed by comparing with the wave force obtained from the fluid analysis. Finally, a sequential structural analysis, with a debris collision phase at the end, was conducted using the ASI-Gauss code to simulate the washout behavior of the building.

COLLAPSE RISK PREDICTION OF BUILDINGS ON FIRE USING KEY ELEMENT INDEX

It is difficult to estimate the redundant strength remaining in a building on fire, since the fire conditions such as their ranges and locations may be different in each case. A large-scale fire occurred on the New York World Trade Center 7 (WTC-7) after the 9.11 terrorist attacks in 2001. The building continued to burn for 7 hours, and ended in a total collapse. The official report on the collapse investigation of WTC-7, released by the National Institute of Standards and Technology (NIST) in 2005, had suggested that the total collapse was triggered by a severe damage of an important column of the building called the key element. On the other hand, there is also an example of a high-rise building on fire that avoided a total collapse, regardless of its main structure continuously heated by fire for a long time; the Windsor building of Madrid in 2005. From the viewpoint of preventing the fire-induced collapse of buildings, it is necessary to clarify the relationship between various structural parameters of buildings, fire locations, their ranges, and the scale of collapse. The purpose of this study is to predict collapse risks of buildings on fire using a key element index (KI). The KI is defined as the ratio of the ultimate yield strengths of the structure with one column eliminated and the initial, undamaged structure. It indicates the contribution of a structural column to the vertical capacity of the structure. We investigated the relationship between the sum of KI values in various cases of fire range and the sum of the height of remains after the collapse. We applied an adaptively shifted integration (ASI) - Gauss code utilizing linear Timoshenko beam elements to investigate the collapse behaviors of a ten-story steel framed building model with various fire patterns. Fracture contact, contact release and re-contact algorithms were implemented in the code. The reduction curves of elastic modulus and yield strength of steel related to elevated temperature, shown by NIST, were adopted to consider the heat effect of fire. Thermal expansion of materials was also considered. From the numerical results of the fire-induced collapse analyses, it is found that the scale of collapse highly depends on fire ranges and locations. The risk of total collapse tends to increase when a large range of fire occurs in the lower layer. In addition, the risk increases much higher in those cases when fire occurs at the peripheral area of the building, compared to those cases at the inner area. The sum of heights of remains seems to depend on the sum of KI values, and there is a specific threshold of the sum of KI values that relates to the initiation of a large scale collapse. Therefore, the sum of KI values may be used to predict and take measures to avoid the risk of collapse under various fire conditions.

有限要素法を用いた地震時における家具の挙動解析

Improperly secured furniture, especially on the upper floors of high-rise buildings under long-period ground motion, can become dangerous objects for human life. Many tumbled furniture such as chairs and desks in schools could become fatal obstacles that obstruct children from evacuating. In this research, an effective numerical code to analyze the motion behaviors of furniture subjected to seismic excitations was developed. The numerical code was developed based upon the adaptively shifted integration (ASI) － Gauss technique, which is a finite element scheme that provides higher computational efficiency than the conventional code. The frictional contact between objects was fully considered by employing a sophisticated penalty method. Some excitation tests of furniture on a shake-table were carried out, where steel cabinets were excited by seismic waves and the displacement data were recorded by a motion capture system. The numerical results were validated by comparing with the shake-table test results.

Seismic pounding and collapse behavior of neighboring buildings with different natural periods

Seismic pounding phenomena, particularly the collision of neighboring buildings under long-period ground motion, are becoming a significant issue in Japan. We focused on a specific apartment structure called the Nuevo Leon buildings in the Tlatelolco district of Mexico City, which consisted of three similar buildings built consecutively with narrow expansion joints between the buildings. Two out of the three buildings collapsed completely in the 1985 Mexican earthquake. Using a finite element code based on the adaptively shifted integration (ASI)-Gauss technique, a seismic pounding analysis is performed on a simulated model of the Nuevo Leon buildings to understand the impact and collapse behavior of structures built near each other. The numerical code used in the analysis provides a higher computational efficiency than the conventional code for this type of problem and enables us to address dynamic behavior with strong nonlinearities, including phenomena such as member fracture and elemental contact. Contact release and recontact algorithms are developed and implemented in the code to understand the complex behaviors of structural members during seismic pounding and the collapse sequence. According to the numerical results, the collision of the buildings may be a result of the difference of natural periods between the neighboring buildings. This difference was detected in similar buildings from the damages caused by previous earthquakes. By setting the natural period of the north building to be 25% longer than the other periods, the ground motion, which hada relatively long period of 2 s, first caused the collision between the north and the center buildings. This collision eventually led to the collapse of the centerbuilding, followed by the destruction of the north building.

Element-size independent, elasto-plastic damage analysis of framed structures using the adaptively shifted integration technique

The adaptively shifted integration (ASI) technique and continuum damage mechanics are applied to the nonlinear finite element analysis of framed structures modeled by cubic Bernoulli–Euler beam elements. A new form of evolution equation of damage, which is a function of plastic relative rotational angles, is introduced in order to remove the mesh-dependence caused by the strain-dependence of damage. The elasto-plastic damage behavior of framed structures can be accurately and efficiently predicted by the combination of the ASI technique and the new damage evolution equation. Some numerical studies are carried out to show the mesh-independence of the proposed computational method.

Effects of Outrigger Truss Systems on Collapse Initiation Times of High-Rise Towers Exposed to Fire

In this paper, progressive collapse analyses were performed on a 30-story, seven-span tower that was exposed to fire. The Adaptively Shifted Integration (ASI)-Gauss technique was used to demonstrate the effects of fire patterns and structural parameters on collapse initiation time: the duration from the beginning of the fire until collapse initiation. Specifically, an outrigger truss system was placed on the roof of a model, and the influence of the system on the structural vulnerability of the tower was verified. The structural parameters that were varied in the analyses included the axial force ratio, the member joint strength ratio and the member strength ratio of the outrigger trusses to the strength of the beams on the first floor. From the numerical results, it is confirmed that collapse initiation times are significantly affected by the member joint strength ratio if the axial force ratio is small (floor loads are low) on the condition that the fire pattern is nearly symmetrical, and the load paths to and from the outrigger truss system are sufficiently protected.

Elastic-Plastic Non Linear Behaviors of Suddenly Loaded Structures

Problem statement: The adaptively shifted integration technique was applied to the elasticplastic analysis of framed structures under dynamic loading. Approach: This study used analysis of linear beam element, the reshifting of the of the integration points in the element is conducted in order to attain higher accuracy. Results: In nonlinear finite element analysis by the ASI technique, the highest computational efficiency has been achieved by shifting the numerical integration points for evaluation of stiffness matrices of linear Timoshenko beam element. A computer program has been Written by VBASIC for solve the problem of the steel frame, results of numerical examples demonstrate the validity of the computer program and study many parametric study, such as Time step and Mass of the structure. Conclusion/Recommendations: In the elastic analysis there is no distinction between the ASI technique and the conventional finite element method, but for elasticplastic nonlinear analysis under dynamic load Adaptive Shifted Integration (ASI) technique is capable of predicting with reasonable accuracy the behavior of steel frame structures.

Finite Element Collapse Analysis of Framed Structures by the Adaptively Shifted Integration Technique

Finite Element Collapse Analysis of Framed Structures by the Adaptively Shifted Integration Technique

Elastic-Plastic Non-Linear Behavior of Suddenly Loaded Plane Steel Frames by ASI Technique

A non-linear finite element method for elastic – plastic analysis of steel plane frames under sudden loading is investigated. Geometric nonlinearity is considered using the Adaptively Shifted Integration (ASI) technique for the linear Timoshenko beam element.In (ASI) technique, the numerical integration point in an elastically deformed element is placed at the optimal point for linear analysis (midpoint in the linear Timoshenko beam), while the integration point is shifted immediately after the occurrence of a fully-plastic section in the element, using the previously established relation between the location of numerical integration point and that of plastic hinge, to form a plastic hinge exactly at the position of that section. Thus the technique produces higher computational accuracy with fewer elements than the conventional finite element code. As a result, the ASI technique gives a more precise solution with fewer elements than the conventional finite element method. The computer program used in this search employs the one –dimensional element with two nodes for steel structures. The major task of the present work is the development of a computer program which incorporates the above method of analysis, and the accuracy of the analytical results is assessed with respect to the available experimental and analytical data.

Structural collapse analysis of framed structures under impact loads using ASI-Gauss finite element method

The main objective of this study is to devise a technique, which, when implemented into finite-element codes, is efficiently applicable to impact collapse analyses of framed structures. In this study, the formerly developed adaptively shifted integration (ASI) technique for the linear Timoshenko beam element is modified into the ASI-Gauss technique by placing the numerical integration points of the two consecutive elements forming an elastically deformed member in such a way that stresses and strains are evaluated at the Gaussian integration points of the two-element member. On comparison with the ASI technique, the ASI-Gauss technique proves its higher accuracy and efficiency in elastic range. Moreover, instead of applying impact loads in the form of nodal forces, we consider the impact phenomenon by means of contacts between the elements involved and the elemental contact algorithm is verified from the point of conservation of energy. Impact analyses considering member fracture with different sets of parameters are performed using a high-rise framed structure and a small aircraft. From the results obtained, we can observe propagation phenomena of impact loads and shock waves. Also, a proper difference in impact damage is obtained by different sets of parameters. The results also indicate that the mass of the aircraft has a stronger influence on impact damage than its velocity. Moreover, soon after impact, tensile stresses are observed in the columns that were compressed by dead loads before impact.

Finite element code for impact collapse problems of framed structures

AbstractThe objective of this study is to develop a dynamic finite element code that can effectively cope with strong non‐linearities and discontinuities common in impact collapse problems, and whose calculation cost is sufficiently low to enable dynamic analyses of full‐model large‐scale structures. The adaptively shifted integration (ASI) technique is modified into the ASI‐Gauss technique to further reduce calculation cost. Algorithms considering member fractures and elemental contact are also presented. Impact collapse analysis is conducted to simulate the aircraft impact with the World Trade Center South Tower (WTC2), and the analytical results showed good agreement with the observed data. Copyright © 2006 John Wiley & Sons, Ltd.

ASI-Gauss法による世界貿易センタービルの飛行機衝突解析

In this paper, the previously developed AST-Gauss technique is applied to an aircraft impact analysis of New York World Trade Center Tower 2 (WTC2), to evaluate the structural vulnerability and behavior of the aircraft, at the horrifying scene that occurred in 2001. The ASI-Gauss technique is a modified version of the formerly developed Adaptively Shifted Integration (ASI) technique for the linear Timoshenko beam element, which computes highly accurate elasto-plastic solutions even with the minimum number of elements per member. The ASI-Gauss technique gains still higher accuracy especially in elastic range, by placing the numerical integration points of the two consecutive elements forming an elastically deformed member in such a way that stresses and strains are evaluated at the Gaussian integration points of the two-element member. From the numerical results, propagation of the shock waves resulted from the impact and high-level stresses in the structural members were observed. We could also see how the main wings of the aircraft cut through the perimeter columns and spandrels, how the debris moved through the building and to where it caused damage. Moreover, the velocity reduction of the right engine and the location from where it moved out of the building were in good agreement with the observed data.

Seismic collapse analysis of reinforced concrete framed structures using the finite element method

AbstractA new finite element code using the Adaptively Shifted Integration (ASI) technique with a linear Timoshenko beam element is applied to the seismic collapse analysis of reinforced concrete (RC) framed structures. This technique can express member fracture as a plastic hinge located at either end of an element with simultaneous release of the resultant forces in the element. Contact between members is also considered in order to obtain results that agree more closely with actual behavior, such as intermediate‐layer failure. By using the proposed code, sufficiently reliable solutions have been obtained, and the results reveal that this code can be used in the numerical estimation of the seismic design of RC framed structures. Copyright © 2003 John Wiley & Sons, Ltd.

Element-Size Independent, Elasto-Plastic Damage Analysis of Framed Structures.

The adaptively shifted integration (ASI) technique and continuum damage mechanics are applied to the nonlinear finite element analysis of framed structures modeled by cubic Bernoulli-Euler beam elements. A new form of evolution equation of damage, which is a function of plastic relative rotational angles, is introduced in order to remove the mesh-dependence caused by the strain-dependence of damage. The elasto-plastic damage behavior of framed structures can be accurately and efficiently predicted by the combination of the ASI technique and the new damage evolution equation. Some numerical studies are carried out to show the mesh-independence of the proposed computational method. presented the formulation for the damage analysis of RC frames by the lumped dissipation model and implemented it in the commercial finite element program. Florez-Lopez (10) gave a unified formulation for the damage analysis of steel and RC frame members. Inglessis et al. (13,14), and Febres et al. (16) conducted the analysis of steel frames considering damage and local buckling in tubular members. Addessi and Ciampi (18) proposed a new beam finite element based on damage mechanics and plasticity to analyze the cyclic structural response of plane frames. However, no discussion has been made for the mesh-dependence of the finite element solutions for the damage problem of framed structures in the existing literatures (6-18). The cubic beam element based on Bernoulli-Euler hypothesis is generally used in the finite element analysis of framed structures neglecting the effect of shear deformation (19). Toi (20) derived the relation between the location of a numerical integration point and the position of occurrence of a plastic hinge in the element, considering the equivalence condition for the strain energy approximations of the finite element and the computational discontinuum mechanics model composed of rigid bars and connection springs. The computational method identified as the adaptively shifted integration technique (21) (abbreviated to the ASI technique) was developed, based on this equivalence condition. The ASI technique, in which the plastic hinge can be formed at the exact position by adaptively shifting the position of a numerical integration point, gives accurate elasto-plastic solutions even by the modeling with the minimum number of elements. The ASI technique has been applied to the static and dynamic plastic collapse analysis of framed structures (21-24), through which the validity of the method has been demonstrated with respect to the computational efficiency and accuracy. In the present study, a new computational method is formulated for the elasto-plastic damage analysis of framed structures, based on the ASI technique for the cubic Bernoulli-Euler beam element and the concept of CDM. The non-layered approach, in which the stress-strain relation is expressed in terms of the resultant stresses and the corresponding generalized strains, is employed in order to reduce the computing time for the large-scale framed structures. A new form of damage evolution equation, which is expressed in terms of the plastic relative rotational angles and the effective element length instead of the plastic curvature changes, is proposed in order to remove the mesh-dependence of solutions in the damage analysis. The present method is applicable to the collapse analysis of framed structures including elasto-plasticity, damage initiation, its evolution and fracture. Numerical studies for simple frames are conducted to show accuracy, efficiency and the mesh-independence of the proposed method.

SEISMIC DAMAGE ANALYSIS OF REINFORCED CONCRETE BUILDING CONSIDERING MEMBER FRACTURE

The Adaptively Shifted Integration (ASI) technique, which produces the highest computational efficiency in the finite element analyses of framed structures including static and dynamic collapse problems, is applied to the seismic damage analysis of a reinforced concrete building. By expressing member fracture by a plastic hinge located at the exact position with a simultaneous release of resultant forces in the element, discontinuous problem such as this kind can be easily analyzed even by the conventional finite element code with the displacemental form. By using the algorithms described in this paper, sufficiently reliable solutions for the practical use have been obtained in the seismic damage analysis of a five stories-five span reinforced concrete building. The present technique can be easily implemented with a minimum effort into the existing finite element codes utilizing the linear Timoshenko beam element.

Analysis of structurally discontinuous reinforced concrete building frames using the ASI technique

The Adaptively Shifted Integration (ASI) technique, which produces the highest computational efficiency in the finite element analyses of framed structures including static and dynamic collapse problems, is applied to structurally discontinuous problems of reinforced concrete building frames. A new numerical scheme based on the updated Lagrangian formulation (ULF) adaptation of the ASI technique is developed, by modeling the fracture of a section by a plastic hinge located at the exact position with a simultaneous release of resultant forces in the element. By using the algorithms described in this paper, the analyses became possible even by the conventional displacement-based finite element codes, and sufficiently reliable solutions for practical use have been obtained in the explosive demolition and seismic damage analyses of a five storied, five span RC building frame. The present technique can be easily implemented with minimum effort into the existing finite element codes utilizing the linear Timoshenko beam element.