Form Intrinsic Finite Element Method Research Articles

Form Follows Force: A theoretical framework for Structural Morphology, and Form-Finding research on shell structures

With the springing up of freeform architectures, the key problem to structural engineers is to generate structural forms with high structural efficiency subject to the architectural space constraints during the conceptual design process. In this research, a theoretical framework for Structural Morphology has been proposed, that provides an effective solution to the problem. To enrich the proposed framework, systematic Form-Finding research on shell structures is conducted.

Form Follows Force: A theoretical framework for Structural Morphology, and Form-Finding research on shell structures

Form Follows Force: A theoretical framework for Structural Morphology, and Form-Finding research on shell structures

Vector form Intrinsic Finite Element Based Approach to Simulate Crack Propagation

AbstractThis paper presents a new approach to simulate the propagation of elastic and cohesive cracks under mode-I loading based on the vector form intrinsic finite element method. The proposed approach can handle crack propagation without requiring global stiffness matrices and extra weak stiffness elements. The structure is simulated by mass particles whose motions are governed by the Newton's second law. Elastic and cohesive crack propagation are simulated by proposed VFIFE-J-integral and VFIFE-FCM methods, respectively. The VFIFE-J-integral method is based on vector form intrinsic finite element (VFIFE) andJ-integral methods to calculate the stress intensity factors at the crack tips, and the VFIFE-FCM method combines VFIFE and fictitious crack models (FCM). When the stress state at the crack tip meets the fracture criterion, the mass particle at the crack tip is separated into two particles. The crack then extends in the plate until the plate splits into two parts. The proposed VFIFE-J-integral method was validated by elastic crack simulation of a notched plate, and the VFIFE-FCM method by cohesive crack propagation of a three point bending beam. As assembly of the global stiffness matrix is avoided and each mass particle motion is calculated independently, the proposed method is easy and efficient. Numerical comparisons demonstrate that the present results predicted by the VFIFE method are in agreement with previous analytical, numerical and experimental works.

Solid structure analysis with large deformation of eight-node hexahedral element using vector form intrinsic finite element

The vector form intrinsic finite element method has been proposed to deal with large deformation and complex non-linear problems in structural analysis. However, the study of method is mainly limited in plane element. This article expands the application range of the vector form intrinsic finite element method by deriving the formula of eight-node hexahedral element. A new method to determine pure nodal deformation was proposed and described in detail, which could simplify the computation comparing to the traditional vector form intrinsic finite element method. Compared with the finite element method and other methods in three different numerical examples, the numerical results of this method show a good reliability and accuracy in large deformation problems. This method lays the foundation for solving three-dimensional solid problems by vector form intrinsic finite element method in structural engineering fields.

Numerical study on critical axial forces of upheaval buckling for initially stressed submarine pipelines on uneven seabed

For pipelines on uneven seabed, upheaval buckling may occur if the axial compressive force reaches the critical force of upheaval buckling. The critical axial force is sensitive to the seabed undulation, However, the effect of the seabed undulation on the critical force has not been completely discussed. Moreover, effect of the initial stress which accumulates in the pipe wall when the pipeline conforms to the seabed undulation under self-weight has been rarely examined. This paper mainly focuses on the effect of the initial stress. Using numerical tools developed with the Vector Form Intrinsic Finite Element (VFIFE) method, effect of the initial stress is proved significant. Subsequently with the theory of dimensional analysis, a formula of the critical axial force is derived. This formula covers the dimensionless undulation length and the Out-of-Straight (OOS) of the seabed undulation. Considering three seabed undulation shapes, coefficients in the formulas are determined with numerical results from the VFIFE simulations. Finally, the proposed formulas are proved applicable for pipes with different properties and within the error range of ±10% for pipelines in continuous contact with the seabed in a large dimensionless scope.

Numerical Modeling of the Configuration of a Long-distance Free-spanning Submarine Pipeline on an Uneven Seabed

In this paper, a procedure is developed to analyze long-distance free-spanning pipelines on an uneven seabed through the incorporation of the Vector Form Intrinsic Finite Element (VFIFE or V-5) method with the bubble model, which is also called the UWAPIPE model. A dynamic contacting scheme is proposed to model variations of the contact situation between a seabed and a deforming pipeline on it. Specifically, a high-efficiency Message Passing Interface (MPI) parallel scheme is adopted to reduce the computing time of the procedure. Through the use of the procedure, the configuration of a 10 km long-distance pipeline lying on a real irregular seabed in the South China Sea is simulated, and the results are compared with a Remotely Operated Underwater Vehicle (ROV) survey and Det Norske Veritas (DNV) recommendations. The effects of the submerged weight and internal pressure of the pipeline are evaluated. Subsequently, the unevenness ratio is defined, and its relation to the pipeline bending moment is presented. The effects of the seabed undulation and adjacent spans are proved to be significant for the examined case.

Application of vector form intrinsic finite element on integrated simulation of wind turbine

SummaryLarge wind turbine system is a periodic time‐varying system with many rigid‐flexible coupling bodies. It is difficult to deal with the singular stiffness matrix produced by the rotation of blades via the traditional finite element method. However, the vector form intrinsic finite element (VFIFE) method can effectively solve the geometric deformation of elastic continuum, the nonlinear or discrete constitutive model, the coupling motion continuum, and rigid body. In this study, a solver program of space beam element is developed by VFIFE method, and three typical examples are chosen to verify its accuracy. And then the integrated simulation of wind turbine system is established, and its dynamic response is analyzed. The natural frequencies of the turbine system, which are obtained by modal parameter identification, can agree well with the results obtained by traditional finite element method. The weighted amplitude wave superposition method and the proper orthogonal decomposition method as well as B‐spline surface interpolation are employed to obtain the wind time series of wind turbine under the normal operation condition. The wind‐induced dynamic response of wind turbine system is calculated by VFIFE method. The numerical results can reflect the periodic influence of gravity on the internal forces of blades and the interaction between blades and the tower.

Analysis of buried pipelines subjected to reverse fault motion using the vector form intrinsic finite element method

Buried pipelines crossing reverse faults is a common case in practice, while their mechanical responses are not very clear. To analyze buried pipelines subjected to reverse faults, a beam-shell coupling scheme is proposed based on the Vector Form Intrinsic Finite Element (VFIFE or V-5) method. Particular emphasis is given to identifying pipeline failure with three performance based limit states: the local buckling, the tensile strain limit and the flattening parameter limit. The critical fault displacements, at which the specified performance criteria are reached, are presented in diagram form. Effects of fault displacement, crossing angle, as well as fault dip angle on critical fault displacements are examined. This study shows that when the fault dip angle is 40°, the critical fault displacements of local buckling and pipe-wall rupture are the largest when a pipeline is oriented approximately parallel to a reverse fault plane. And for a perpendicularly crossing pipeline, the smaller the dip angle is, the more severe the cross-section distortion will be. Moreover, the critical strain of local buckling are obtained and compared with the recommendation of CSA Z662.

Vector form intrinsic finite element method for planar multibody systems with multiple clearance joints

A new computational methodology is presented for the dynamic analysis of multibody systems with multiple clearance joints by vector form intrinsic finite element method. A joint model is developed to simulate the motion of ideal and clearance joints for multibody systems. The dynamic behaviour of a four-bar mechanism with three clearance joints in continuous contact mode is analysed. The results show that the dynamic performance of the mechanism with three clearance joints in continuous contact mode is not similar to that with ideal joints and is fluctuating and affected by the clearance size of the joints and input crank speed.

Nonlinear Vibration Analysis of Membrane SAR Antenna Structure Adopting a Vector Form Intrinsic Finite Element

ABSTRACTThis study adopted the Vector Form Intrinsic Finite Element (VFIFE) method to study the nonlinear vibration of the membrane SAR (Synthetic Aperture Radar) antenna structure. As the dynamic characteristic of the antenna is mainly determined by the support frame, it can be simplified as an axially loaded cantilever beam. The linear and geometrically nonlinear models of the axially loaded cantilever beam are established. The beam is modeled as discrete mass points which are connected by deformable elements through VFIFE method. A statics analysis is first presented to verify the VFIFE method. Then effects of the geometrical nonlinearity and axial load are investigated. It is believed that the presented study is valuable for better understanding the influences of the geometrical nonlinearity and axial load of the cantilever beam on the structural vibration characteristics.

Ultimate State of Bridges with Soil-Pile-Structure Interaction under Extreme Earthquakes

This paper is aimed to analytically study the ultimate state of bridges with seismic soil-pile-structure interaction. Since the Vector Form Intrinsic Finite Element method is superior in managing highly nonlinear engineering problems even with fracture and collapse, it is used in this study to predict the failure process of bridges. During an extreme earthquake, soil may undergo plastic behavior, and piles may go through cracking, plastic hinge, even fracture. In this study, several nonlinear soil-spring models are developed to simulate the soil-structure interaction behavior under strong ground motions. Through a series of parametric studies, the failure modes are demonstrated for bridges with pile foundation. The result showed that, both soil and piles went through plastic behavior. It is suggested to analyze bridges under strong ground motions by using nonlinear soil elements for realizing the actual dynamic behavior.

Ultimate State of Bridges with Rocking Isolation under Extreme Earthquakes

This study is aimed to analyze the ultimate state of bridges with rocking isolation of spread foundations under extreme earthquakes. The Vector Form Intrinsic Finite Element method (VFIFE) is adopted to simulate the failure procedure of bridges with and without rocking isolation. To simulate the highly nonlinear behaviors between soil and foundations, Winkler-based models are established in the VFIFE in this study. A practical five-span bridge with spread foundations is chosen to study the effect of rocking isolation and discuss the influence of altering parameters of bridges. The analytical results are compared between linear soil springs and nonlinear soil springs. Furthermore, the ultimate state of bridges is simulated to realize the dynamic behaviors of bridges under extreme earthquakes.

Entire-Process Simulation of Earthquake-Induced Collapse of a Mockup Cable-Stayed Bridge by Vector Form Intrinsic Finite Element (VFIFE) Method

It is important to simulate the entire-process collapse of earthquake excited cable-stayed bridge in order to assure the damage extent under strong earthquakes and to optimize the anti-collapse seismic measures. The newly developed vector form intrinsic finite element (VFIFE) method is capable of computing large deformation, large displacement, collision, and fractures that would happen in the structural collapse. Therefore, it has the potential to simulate the entire-process collapse of earthquake excited structures. For the cable-stayed bridges, the axial forces change significantly during the earthquake excitation. The interaction between the axial forces and bending moments should be taken into account. In order to address this issue, this paper first presents the formulation for integration of VFIFE method and fiber beam-column element model. A bilinear elastic-plastic constitutive damage model is proposed for the mechanical behavior of the fiber and element. The collapse analysis of a 2D mockup bridge scaled from an actual cable-stayed bridge is then conducted. The entire process of the structural damage and collapse are successfully simulated by the proposed method VFIFE-Fiber. This study provides a foundation for seismic damage prediction and anti-collapse seismic design for cable-stayed bridges.

Nonlinear Analysis of the Motion Structures

In this paper, the nonlinear analysis of the motion structures is studied by using the vector form intrinsic finite element (VFIFE, V-5) method. The main object of this research is to develop an internal hinge of two ends of the plane frame element. In this study, the hinge function of frame element is used to compute the nonlinear dynamic responses of the motion structures. A fictitious reversed rigid body motion can be used to separate the rigid body motions and the pure deformations of the frame element. It is not requires any iteration or any parameters for the VFIFE method during computation process. Four examples illustrate the accuracy of the proposed procedures in computing large motions of a flying flexible structure.

Application of Gap Element Method to Wheel/Rail Contact Problem Based on V-5

The vector form intrinsic finite element (V-5) method and the gap element method are combined to solve the static wheel/rail contact in two-dimensions in this paper to obtain the wheel/rail normal contact pressure, which would be compared with the normal contact pressure of ABAQUS and Hertz theory. The results showed that the contact pressure distribution of V-5 was consistent with ABAQUS and Hertzs, and the mechanical behavior of contact area was reasonable under the circumstance of different axle loads. Besides, it also verified the feasibility of adopting gap elements method to solve the static wheel/rail contact on the basis of vector form finite element method, which with the superiority of large rotation and large deformation, and laid the foundation of rolling wheel-rail contact behavior analysis.

Failure Analysis of a Cable Dome Due to Cable Slack or Rupture

Cable dome is a new type of spatial structure, consisting of cables and struts. Its properties such as its static, dynamic and stability behavior were widely studied, but the failure of the dome is rarely investigated due to its complexity and the limitation of traditional methods. The Vector Form Intrinsic Finite Element method (VFIFE) is a recently proposed method based on a combination of vector mechanics and numerical calculation. Without establishing the stiffness matrix, it is easy to solve problems related to rigid body motion, large deformation and large displacement. It is thus used to simulate the whole failure process of cable domes. The fundamentals of VFIFE are first summarized and the formulations for rod elements and prestressed cable elements are presented. Then the failure analysis of a dome due to cable slack or rupture is conducted by taking a Levy cable dome as an example. Numerical results show that the dome can continue to bear load after some cables slack and will fail after some hoop cable rupture. The dynamic effects caused by cable rupture should not be ignored. Numerical results also indicate that the VFIFE method is effective in the full-process analysis of structures involving rigid body motion, large deformation or vibrations.

Analysis of Elastic Beam Subjected to Moving Dynamic Loads

The main object of this paper is to apply the vector form intrinsic finite element (VFIFE, or V-5) techniques in nonlinear large deformation dynamic analysis for the responses of moving loads on rigid frame structures. In this study, the simulation of moving loading is brought into the vector form intrinsic finite element method. It can effectively simulate the moving load. Comparing the results of the numerical simulations by VFIFE with the results obtained from other literatures, they are very close. It proved that VFIFE can effectively simulate the nonlinear large deformation dynamic problem.

Vector Form Intrinsic Finite Element analysis of nonlinear behavior of steel structures exposed to fire

This study adopted the Vector Form Intrinsic Finite Element (VFIFE) method to study the nonlinear fire response of steel structures. The numerical model is first verified by comparing the results with the published experimental and analytical results for steel structures. The nonlinear behavior of the fire response of the Williams toggle frame, and the steel frames subjected to earthquake load and fire load are then fully studied. The numerical results show that the bearing capacity of the Williams toggle frame rises markedly with the increase in temperature when the temperature is less than the critical value. However, when the temperature is more than the critical value, the bearing capacity of the Williams toggle frame decreases with the increase in temperature, but its bearing capacity at 1000 ∘C is still larger than the elastic buckling strength at room temperature. In addition, the shallow arch deflects upward before buckling with increasing temperature, and its deflection is much smaller than that of the beam structure with the same span. The structure deflects downward after buckling and shows catenary action when it is re-balanced. In the case of fire induced by an earthquake, the deformation of the structure is significantly affected by the aftershock, fire, and fracture of structural elements.

Nonlinear behavior of steel structures considering the cooling phase of a fire

The nonlinear behavior of steel structures considering the heating and the cooling phases of a fire is investigated by the Vector Form Intrinsic Finite Element (VFIFE) method. The temperature dependent constitutive relations of steel which include strain reversal effects are adopted. The numerical model is first verified by comparing the results with the published analytical and experimental results for steel structures in the cooling phase. Several numerical examples are then fully studied to investigate the cooling behavior of steel structures. The proposed numerical model can effectively predict the nonlinear behavior of the steel structure in both the heating and cooling phases.

Nonlinear Dynamic Analysis of Reticulated Space Truss Structures

AbstractIn this paper, a simpler formulation for the nonlinear motion analysis of reticulated space truss structures is developed by applying a new concept of computational mechanics, named the vector form intrinsic finite element (VFIFE or V-5) method. The V-5 method models the analyzed domain to be composed by finite particles and the Newton's second law is applied to describe each particle's motion. By tracing the motions of all the mass particles in the space, it can simulate the large geometrical and material nonlinear changes during the motion of structure without using geometrical stiffness matrix and iterations. The analysis procedure is vastly simple, accurate, and versatile. The formulation of VFIFE type space truss element includes a new description of the kinematics that can handle large rotation and large deformation, and includes a set of deformation coordinates for each time increment used to describe the shape functions and internal nodal forces. A convected material frame and an explicit time integration scheme for the solution procedures are also adopted. Numerical examples are presented to demonstrate capabilities and accuracy of the V-5 method on the nonlinear dynamic stability analysis of space truss structures.