Nonlinear Quasi-static Analysis Research Articles

A framework for implementing structural integrity management of an aging fixed offshore platform using wave modeling for risk-based underwater inspection provision

Offshore platforms have become lucrative in the oil and gas industries due to their capabilities, which are exposed to harsh environmental hazards that affect the Structural Integrity.The scope of this study represents a risk assessment strategy for evaluating the structural integrity and proposed a framework for the Risk-Based Underwater Inspection to implement Structural Integrity Management for a fixed offshore jacket platform.The jacket platform is adopted for the Non-linear Quasi-Static Analysis (Push-over) using relevant code criteria. Regarding the required site-specific meteorological and oceanographic parameters, wave is simulated using WAVEWATCH III, third-generation version 4.18, considered input data and uncertain parameters.The Long-Term Load Distribution parameters are localized to determine the Probability of Failure due to the extreme wave loading action, and the platform structural damage rate is obtained by referring to the latest available underwater inspection carried out in the understudied oilfield. Moreover, the platform's structural failure may lead to safety, environmental, and economic impacts, which are the essential factors for evaluating the Consequence of Failure.Finally, the risk level is estimated by ranking the Probability and Consequences of Failure in the risk matrix, and resulting from the risk analysis, the framework for the Risk-Based Underwater Inspection is carried out.

DINAMIC FORCES IN THE ECCENTRICALLY COMPRESSED MEMBERS OF REINFORCED CONCRETE FRAMES UNDER ACCIDENTAL IMPACTS

Interest to solving scientific problems related to the evaluation of facilities' resistance and its protection against progressive collapse increases and attracts more and more attention of specialists in the field of structural analysis and design. Therefore, the article presents the results of a computational analysis of dynamic forces in eccentrically compressed reinforced concrete members of structures under accidental impact such as sudden removal of a load bearing member. Using relations for specific deformation energy and integrating it through the cross-section area, the analytical expressions for dynamic strains and curvatures have been obtained for physically and structurally nonlinear RC frame members under eccentric compression. These expressions in some cases allow symbolic solution, for example, in MathCAD software. In contrary, it can be solved with the approximate iterative method. To assess the reliability and effectiveness of the proposed quasi-static method, the analysis of the cast-in-situ reinforced concrete frame resistance to progressive collapse has been performed. The article also provides comparison of the simulation results of the nonlinear quasi-static analysis and the nonlinear dynamic time-history analysis.

Weak-form differential quadrature element analysis of plate on a tensionless and frictional foundation using a higher-order kinematics

Plate-foundation systems, as a structure common in engineering practices, have received extensive scientific research. A novel technical scheme is proposed to improve the computational efficiency in predicting the nonlinear responses of a plate on the foundation. The core work of this technical scheme lies in two aspects. The first aspect is to create a novel plate-foundation system, where a higher order kinematical assumption common in Carrera Unified Formulation is used to model the plate, and a plate-foundation interaction model taking into account the tensionless and frictional characteristics is created. The adjustable kinematical parameters of the higher-order kinematical assumption endow the plate with flexible accuracy. The second aspect is to derive a two-dimensional (2D) differential quadrature (DQ) formula for 2D interpolation based on the one-dimensional (1D) DQ formula, and thus a weak-form differential quadrature element method (WDQEM) for nonlinear quasi-static analysis of the plate-foundation system is proposed by using the principle of virtual work and the 2D interpolation derived. The proposed WDQEM supports flexible nodal configuration in the element, making it degree-of-freedom-flexible and suitable to carry out both p- and h-version strategies in the numerical simulation. Several numerical examples are given to (i) verify the proposed technical scheme and the corresponding computer codes; (ii) to investigate the numerical performance of the WDQEM through comparison between the classical plate model and the 3D solid model, and (iii) to study some physical behaviors related to the tensionless and frictional characteristics of the plate-foundation system. The example results show that (i) the WDQEM converges much faster than the conventional finite element method due to the higher order approximation; (ii) the higher order kinematics, due to its capability of adjusting the accuracy of kinematical assumptions, can effectively reduce the computational scale; (iii) the smoothness problem in the post process of stresses analysis is greatly alleviated, (iv) the tensionless and frictional features of the plate-foundation system should be considered when evaluating both the vertical and horizontal bearing capacities of the plate.

Nonlinear Seismic Assessment of a Historic Rubble Masonry Building via Simplified and Advanced Computational Approaches

This research presents a comprehensive nonlinear quasi-static seismic assessment of an unreinforced rubble masonry building, Bytown Museum in Ottawa, Canada, using discontinuum-based analyses. In the proposed modeling approach, non-uniform geometrical properties of rubble masonry walls are replicated via a group of rigid polyhedral blocks interacting along their boundaries based on the discrete element method (DEM). Once the adopted modeling strategy is validated, the nonlinear quasi-static analysis of the South and North façades of the Bytown Museum is performed. Special attention is given to the irregular block generation within the discontinuum analysis framework, where discrete element models are generated from high-resolution site recording data, representing the masonry morphology at a high level of detail. Then, the predicted collapse mechanisms from advanced computational models are further utilized to generate pre-defined macro-blocks in kinematic limit analyses, providing a simple alternative solution for seismic assessment. The results reveal the significant effect of openings and the construction technique (morphology) in unreinforced rubble masonry buildings that can play an important role in the structural capacity and behavior. Moreover, it is noted that DEM-based solutions provide lower seismic capacity compared to kinematic limit analyses. Finally, a noticeable sensitivity to the input parameters in the discrete element models is noted; therefore, characterization of material properties is necessary for reliable predictions.

Strength, stiffness, ductility, and dissipated energy reduction of semisupported steel shear walls (SSSW) due to a circular opening

SummarySemisupported steel shear walls (SSSWs) with web plates that are only connected to the beams were proposed as a means of mitigating column demands. In this research, equations for evaluating the reduction factors of performance characteristics (i.e., shear strength, initial stiffness, ductility, and energy dissipation) for SSSWs with the circular opening at the center are proposed. Nonlinear quasistatic analyses under cyclic loading were conducted on a series of perforated SSSWs with different slenderness ratio and different perforation diameters to assess the effectiveness of the proposed equations. Based on the results, the performance characteristics of SSSWs are affected directly by the square D/LPTF (D and LPTF are the perforation diameter and the length of the partial tension field along the beam, respectively). Furthermore, the proposed equations underestimate the reduction factors for web plates with higher perforation ratios, D/H (H is the height of web plate). With an increase in the perforation ratio, deterioration of shear strength and dissipated energy is so severe compared with that of initial stiffness and ductility factor. The proposed equations for performance characteristics deterioration have been validated by the good correlation between predicted values and experimental data.

Ductile behavior of existing internal end diaphragms in steel tub girder bridges

In steel tub girder bridges, end diaphragms transmit vertical and lateral loads to the substructure. Vulnerable response of steel diaphragms in recent strong ground motions has encouraged the researchers to work on their application as seismic force reducing devices for design and retrofitting of bridges. This study is an attempt to achieve a ductile diaphragm behavior under seismic actions by using existing internal end plate diaphragm of steel tub girder bridges. Considerable elastic stiffness and dominant shear behavior of the end diaphragm has made it a suitable choice for such behavior under seismic actions. Nonlinear quasi-static analyses using nineteen different finite element models were conducted to evaluate the internal end diaphragm behavior with different configurations and boundary elements. Moreover, plastic analyses using tension strips theory were used to derive formulations for design base shear and tension field inclination of different models. The calculated values were in agreement with the results of finite element models. As a result, remarkable response modification factor was derived for the proposed ductile system. In addition, nonlinear time history analyses were used to prove the ductile behavior of the selected models under real moderate and strong ground motions.

Nonlinear quasi-static analysis of ultra-deep-water top-tension riser

In order to analyse the ultra-deep-water top-tension riser deformation in drilling conditions, a nonlinear quasi-static analysis model and equation are established. The riser in this model is regarded as a simply supported beam located in the vertical plane and is subjected to non-uniform axial and lateral forces. The model and the equation are solved by the finite element method. The effects of riser outside diameter, top tension ratio, sea surface current velocity, drag force coefficient, floating system drift distance and water depth on the riser lateral displacement are discussed. Results show that the riser lateral displacement increase with the increase in the sea surface current velocity, drag force coefficient and water depth, whereas decrease with the increase in the riser outside diameter, top tension ratio. The top tension ratio has an important influence on the riser deformation and it should be set reasonably under different circumstances. The drift of the floating system has a complicated influence on the riser deformation and it should avoid a large drift distance in the proceedings of drilling and production.

Deteriorating hysteresis model for cold-formed steel shear wall panel based on its physical and mechanical characteristics

Shear wall panels (SWP) are the primary lateral load resisting elements in cold-formed steel (CFS) structures. In this paper, smooth hysteresis models that take into account strength and stiffness degradation, as well as pinching effect have been developed and implemented in OpenSees software, as user-defined uniaxial materials named CFSWSWP and CFSSSWP for wood and steel sheathed SWP, respectively. The proposed analytical models are validated using the experimental tests results obtained from the literature, where a good agreement has been achieved. In order to investigate the influence of the CFS SWP parameters variation on the hysteresis characteristics of the response, several non-linear quasi-static analyses have been carried out using different CFS SWP configurations. The key parameters which have most affected the cyclic response were identified and assessed.

Nonlinear quasi-static analysis of hybrid sliding–rocking bridge columns subjected to lateral loading

In this paper, a nonlinear three-dimensional finite element (FE) model for a hybrid sliding–rocking (HSR) column is developed. The HSR columns are segmental members incorporating internal unbonded post-tensioning, rocking joints at the member ends, and intermediate sliding joints along the member height. The HSR columns introduce new design parameters (e.g., frictional properties at the sliding joints, amplitude of joint sliding, number/distribution of sliding joints along the column height) and additional modeling challenges (e.g., contact interactions between adjacent segments and between segments and the internal unbonded post-tensioning tendons) as compared with conventional monolithic or rocking-only members. In the proposed modeling approach, contact interaction amongst adjacent segments and between segments and unbonded tendons are captured. Concrete segments are modeled using solid elements, mild steel reinforcement is modeled by beam elements embedded into the concrete segments, and the unbonded tendons are modeled using truss elements. The FE model was validated against available experimental data and was then used to conduct a parametric pushover study. Variations of the external vertical load were found to have minor effects on the lateral column response. Increase of the initial post-tensioning force resulted in early onset of inelastic response of the tendons, while the peak lateral column strength remained unchanged. Joint sliding increased the lateral deformation capacity of the column. Propagation of sliding from bottom to top and vice versa had small effects on the lateral response of the column. Propagation of sliding was controlled by the friction properties at the sliding joints.

Comparisons of Linear and Nonlinear FEA of Adhesively Bonded Beams

The effect of boundary conditions on the stress distributions in single-lap adhesively bonded cantilevered beams has been investigated using the three-dimensional linear static and non-linear quasi-static finite element method. The displacement obtained from the linear static and the non-linear quasi-static analyses are compared under the same deformation scale factor for three typical boundary conditions. The analysis results indicate that there are significant differences between the linear static and non-linear quasi-static analyses only if there are significant bending effect on the bonded section. The bigger the bending effect on the bonded section, the bigger the difference between the linear static and non-linear quasi-static analyses.

A novel updated Lagrangian complementary energy-based formulation for the elastica problem: force-based finite element model

This paper addresses the development of a novel updated Lagrangian variational formulation and its associated finite element model for the geometrically nonlinear quasi-static analysis of cantilever beams. The formulation is based on an incremental complementary energy principle. The proposed finite element model only contains nodal bending moments as degrees of freedom. The model is used for the analysis of problems modeled by the so-called elastica theory. Numerical solutions satisfying all equilibrium equations in a strong sense can be obtained for arbitrarily large displacements and rotations. A Newton–Raphson method is adopted to trace the post-buckling response. Numerical results are presented and compared with those produced by the standard total Lagrangian two-node displacement-based finite element model.

Three-Dimensional Non-Linear FE Analysis of Shear Stress Distributions in Adhesively Bonded Joint

The aim of this work is to investigate the shear stress distributions across the adhesive layer thickness in single-lap adhesively bonded joint. The shear stress distributions of a single-lap adhesively bonded joint have been investigated using the three-dimensional linear static and non-linear quasi-static finite element method. The analysis results indicate that there are significant differences between the linear static and non-linear quasi-static analyses. The results also show that the maximum value of the shear stress component S13 occurs at the centre line while the maximum of the shear stress components S12 and S23 occur near or at the left-rear corner of the adhesive layer.

Evaluation of Flood-Resistant Capacity of Scoured Bridges

AbstractThe exposure of pier foundations owing to scour significantly reduces the foundation-bearing capacity and diminishes the flood-resistant capacity of a bridge. This paper proposes a nonlinear quasi-static analysis procedure for the performance of bridges with pile foundations under flow-induced loads for the evaluation on the flood-resistant capacity of scoured bridges. The Winkler beam model is adopted for the modeling of the pile-soil system, and the distributed hinge model is utilized to simulate the possible flexural failure of the piles. Soil springs with nonlinear p-y curves are used to represent the nonlinearity of the supporting soil. To demonstrate this procedure, a case study on the Shuang-Yuan Bridge in Taiwan was performed for various flood and scour conditions. This bridge was partially demolished in a major flood event caused by Typhoon Morakot in 2009. According to the analysis results, a possible scenario for the failure of the Shuang-Yuan Bridge is presented, and the proposed metho...

Explicit dynamic formulation to demonstrate compliance against quasi-static aircraft seat certification loads (CS25.561) – Part II: Influence of body blocks

Loading an aerospace and automotive seat statically through lap or body blocks is a complex and highly non-linear problem, as the key numerical challenge is to replicate the contact and slipping kinematics between seat, lap block and belt. In addition, severe element distortions and unexpected contact between parts can occur due to the large deformations involved, which result in implicit solvers struggling to find a converged solution. This paper focuses on the use of an explicit Finite Element Analysis (FEA) solver (LS-DYNA3D) for an aircraft seat subject to Certification Specifications CS25.561, although the ideas presented are equally applicable to automotive seat designers. Explicit codes are better able to overcome contact convergence issues and are often used with appropriate damping to achieve a quasi-static solution. This paper reviews the methodology presented in Part I, whereby issues relating to damping, mass and time scaling are outlined in order to overcome the high computational time step costs (Courant-Friedrichs-Lewy (CFL) condition), together with the procedural and error checks required to ensure a quasi-static response. This paper extends the methodology by considering load cases that use lap blocks, such as ‘forward 9g’ and ‘upward 3g’ certification requirements. Alternative modelling approaches to represent the loading mechanism and effect of lap block mass on solution accuracy are discussed. This paper concludes with a verification framework that outlines the quality checks on various model energies and their ratios, where the numerical results are validated against test in terms of displacements and seat kinematics. Thus, ‘Part I’ and ‘Part II’ cover all elements related with the application of an explicit dynamic integration scheme to demonstrate static seat compliance, and together, form a clear framework to assist a Computer Aided Engineering (CAE) analyst involved in applying an explicit integration scheme to solve non-linear quasi-static analyses.

Residual Stress Analysis by Mutiple Sequential Coupling for Non-Scallop Welding Joint

In this paper, the non-scallop welding joint as the research object is analyzed by ABAQUS software where the implicit analysis method is used to define the residual stress distributions. Based on the thermal analysis, the non-linear quasi-static analysis is also taken, and then the results are compared with the experimental results. The results demonstrated higher accuracy of the finished simulation.

Modelling inelastic hinges using CDM for nonlinear analysis of reinforced concrete frame structures

A new formulation based on lumped plasticity and inelastic hinges is presented in this paper for nonlinear analysis of Reinforced Concrete (RC) frame structures. Inelastic hinge behaviour is described using the principles of Continuum Damage Mechanics (CDM). Member formulation contains provisions to model stiffness degradation due to cracking of concrete and yielding of reinforcing steel. Depending on its nature, cracking is classified as concentrated or distributed. Concentrated cracking is accounted through a damage variable and its growth is defined based on strain energy principles. Presence of distributed flexural cracks in a member is taken care of by modelling it as non-prismatic. Plasticity theory supported by effective stress concept of CDM is applied to describe the post-yield response. Nonlinear quasi-static analysis is carried out on a RC column and a wide two-storey RC frame to verify the formulation. The column is subjected to constant axial load and monotonic lateral load while the frame is subjected to only lateral load. Computed results are compared with those due to experiments or other numerical methods to validate the performance of the formulation and also to highlight the contribution of distributed cracking on global response.

Fatigue failure investigation on anti-vibration springs

Fatigue failure investigation on anti-vibration springs, involving both metal and rubber materials, is presented. Rubber-to-metal bonded springs are widely used in industry as anti-vibration components giving many years of service. Recently a need to improve time and cost efficiencies has caused an unexpected early fatigue failure of the component with no immediate explanation. The required total fatigue life was 1.25 million cycles but only 0.7 million cycles achieved. There was an urgent need to investigate the causes of the fatigue failure and to modify the component design accordingly to meet the customer requirement and the supply schedule. The investigation, based on the actual fatigue loads, is carried out on these failed and modified products using a method of continuum mechanics. To simplify the simulation, a non-linear quasi-static analysis is carried out and then the residual stresses are superimposed to obtain the effective stress range to predict the metal crack initiation. For the rubber parts a three-dimensional effective stress criterion is employed to predict the fatigue crack initiation. The fatigue failure is taken as visual crack observation (normally 1–2 mm). The fatigue crack initiation for the metal parts of the failed component is predicted at 225 K cycles under specified fatigue load against total metal broken at 700 K cycles from the test. For the modified part the minimum total fatigue life for the metal parts of the component, estimated conservatively, is 2.1 million cycles against 1.75 million cycles from the test without any crack observed. The rubber fatigue crack initiation is predicted at 90 K cycles against crack onset around 79 K cycles and crack length 40 mm at 145 K cycles from the test. From design point of view it is important to optimize the rubber profile under this very tight allowable space to provide the maximum support of the metal interleaves and at the same time to meet the minimum requirements of the manufacture process. It is shown that this approach can be employed at a design stage for both metal and rubber fatigue evaluations on anti-vibration springs.