Nonlinear Static Analysis Method Research Articles

Geometric Non-Linear Analysis of Composite Laminated Plates Using Higher Order Finite Strip Element

A finite strip method for geometric non-linear static analysis based on the tangential stiffness matrix has been developed using the new concept of polynomial finite strip elements, with Reissner (higher order shear deformable element) plate-bending theory for composite plates. A finite strip analysis programming package, which is capable of performing non-linear analysis for composite flat panels, has also been developed with Reissner plate bending element. Good agreement with the finite element results has been observed through various test cases, confirming the accuracy and reliability of the new developed finite strip method.

Second-order plastic-hinge analysis of space semi-rigid steel frames

This paper presents a numerical procedure based on the beam–column method for nonlinear static analysis of space semi-rigid steel frames. The second-order effects are considered by the use of stability functions obtained from the exact solution of beam–columns under end forces and the inelastic behavior of material are presented by the lumped inelastic concept using yield surface. An independent zero-length element comprising of six translational and rotational springs, of which rotational spring stiffness uses the Kishi–Chen power model, is used to simulate the rigidity of the steel beam-to-column connection. The generalized displacement control method is applied to solve the nonlinear equilibrium equations in an incremental–iterative scheme. The nonlinear response results are compared with those of existing studies to verify the accuracy of the proposed numerical procedure.

Assessment of Nonlinear Static Procedures for Determination of Target Displacement in Asymmetric Buildings

The conventional procedure for pushover or non-linear static analysis (NSA) has some drawbacks in predicting the inelastic seismic demands of buildings which are asymmetric in plan. In this research, fifteen asymmetric buildings comprising of steel moment frames have been designed and their seismic responses have been studied by pushover analysis. Using methods proposed in FEMA-356, ATC-40, and FEMA-440, the target displacements for these structures have been obtained. Subsequently pushover analyses have been repeated using lateral forces corresponding to 100% of target displacement in principal direction and 30% of target displacement in perpendicular direction. Results of this study indicate that target displacements results from FEMA-440 methods for the roof center of mass ( CM) are closest to the NTHA results but displacements obtained for the stiff side of structure in all NSA methods are underestimated. Therefore a correction factor has been derived using the Least Squares Method to modify the demand displacements obtained from pushover analysis for the stiff side of asymmetric buildings.

Maximum-entropy meshfree method for nonlinear static analysis of planar reinforced concrete structures

A meshfree method for nonlinear analysis of two-dimensional reinforced concrete structures subjected to monotonic static loading is presented. The concrete model is implemented in the context of the smeared rotating crack approach. The stress–strain relationship for steel bars accounts for the surrounding concrete bonded to the bar (tension stiffening effect). The principle of virtual work (variational form) is used to setup the nonlinear system of equations. Maximum-entropy basis functions are used to discretize the two-dimensional domain and background cells are adopted to facilitate the numerical integration. The generalized displacement control method is implemented to solve the nonlinear system of equations and to obtain the softened structural response beyond the maximum load capacity. The proposed meshfree methodology is used to study the nonlinear behavior of reinforced concrete shear walls. Comparisons with experimental data and finite element analysis indicate that the proposed maximum-entropy meshfree method is a viable approach for nonlinear simulations of planar RC structures.

Assessment of Using of Knee Bracing in Retrofitting of Existing Steel Structures with Special Moment Resistant Frame System (Technical Note)

In this paper, non-linear behaviors of structures with special moment resistant frame were studied and possibility of using knee bracing for retrofitting of those structures was examined. For this aim, the structures that have been designed according to the second edition of Iranian seismic code (2800), were selected. Those models have 3, 5 and 7 stories. To evaluating and retrofitting of models, non-linear static analysis and capacity spectra (ATC-40) method were applied and providing of the expected performance levels in FEMA356 was studied. Results showed that the response of structures that designed according to the previous edition of code (second edition) is not compatible with the criteria of third edition. The knee bracing system was used to seismic retrofit of those structures. It would be concluded that the using of knee bracing increases lateral stiffness and improves their energy dissipating capacity. Furthermore, the results showed that the shorter knees have the highest stiffness and ductility in the structures.

Survey on different factors influencing small-scale milking practices in a peri-urban area

The main objective of this paper is to evaluate the load-displacement capacity of steel moment-resisting frame structures using the conventional non-linear static analysis method and incremental dynamic analysis approach. Emphasis was put on the influence of different lateral load patterns on the plastic hinge of structural components and also on the seismic behavior of the structures which is influenced by the behavior of their components [(EEsof, electronic engineering software)]. Firstly, to get an idea, two simple frames were selected and analytically tested using the conventional push-over and then the results were compared with dynamic analysis approach using a simple harmonic time-history. The results show that the axial forces in columns obtained from dynamic approach are smaller than those of the other non-linear static methods and this influences the plastic hinge lengths. Then three sets of steel moment-resisting frames were loaded under different load patterns frequently used in conventional push-over analysis methods. The outputs of the structural analysis, in the forms of story shear versus story drift ratios of upper, middle and lower portions show that in general, nonlinear static analysis results in smaller axial forces in columns which cause smaller component deformations, thus weaker structural load-deformation capacities. Key words: Performance- based engineering,nonlinear static analysis, lateral load pattern, plastic hinge.

Topology Optimization for Structures With Nonlinear Behavior Using the Equivalent Static Loads Method

Many structures in the real world show nonlinear responses. The nonlinearity may be due to some reasons, such as nonlinear material (material nonlinearity), large deformation of the structures (geometric nonlinearity), or contact between the parts (contact nonlinearity). Conventional optimization algorithms considering the nonlinearities are fairly difficult and expensive because many nonlinear analyses are required. It is quite difficult to perform topology optimization considering nonlinear static behavior because of the many design variables. In the current element density based topology optimization considering nonlinear behavior, low-density finite elements cause serious numerical problems due to excessive mesh distortion. Updating the material of the finite elements based on the density is considerably complicated because of the relationship between the element density and structural material. The equivalent static loads method for nonlinear static response structural optimization (ESLSO) has been proposed for size and shape optimization. The equivalent static loads (ESLs) are defined as the linear static load sets which generate the same displacement field from nonlinear static analysis. In this research, a new algorithm is proposed for topology optimization considering all kinds of nonlinearities by modifying the existing ESLSO. The new ESLSO can overcome the difficulties which may occur in topology optimization with nonlinear static behavior. A nonlinear static response optimization problem is converted to cyclic use of linear static response optimization with ESLs. Therefore, the new ESLSO can generate results of nonlinear static response topology optimization by using well established nonlinear static analysis and linear static response topology optimization methods. Four structural examples are demonstrated using the finite element method. Different kinds of nonlinearities are involved in each example.

Evaluation of the Torsional Response of Multistory Buildings Using Equivalent Static Eccentricity

The equivalent static eccentricities of seismic forces are usually defined by building codes with simple expressions of the static eccentricity. The inelastic torsional response of multistory buildings using nonlinear static analysis (NL-SA) with the equivalent static eccentricities is less easily predictable because the response is influenced by the extent of plastic deformations, and the eccentricity varies story by story at each step. To overcome this weakness, it is necessary to change the location of static eccentricity in each step of the NL-SA method. In this paper, a simplified procedure for the correct calculation using the NL-SA method with varying static eccentricity based on the modal response of a single-story scheme is presented. In order to estimate torsional effects on the seismic response, the associated plastic mechanism is developed in a three dimensional model of building, using an updated version of the DRAIN-3DX program. The torsional response of three different structural systems wi...

A PRACTICAL METHOD FOR DETERMINATION OF THE PUSHOVER CURVES

In recent years, performance analysis of the structures has become more of an issue, in parallel with the developments in earthquake engineering. Different types of methods are developed for the assessment of the performance of the structures under earthquake loads. Among these methods,due to being uncomplicated, nonlinear static analysis methods became prominent and took parts in Earthquake Codes. In nonlinear static analysis methods, pushover curve is used to identify the behavior of a structure. In this study a practical method for the determination of the pushover curves of multistory structures is suggested. In the study initially the method and the assumptions are presented afterwards examples are solved to investigate the reliability of the method. In the examples, static pushover curves are obtained by the proposed method and compared with the pushover curves which are obtained by detailed method. Comparison of the results indicates that the ones obtained by the presented method are in good agreement with the ones which are obtained by detailed method.

Determination of Behavior Coefficient of Prefabricated Concrete Frame ith Prefabricated Shear Walls

Increasing population in recent decades has made the necessity of quick low cost construction unavoidable. Meanwhile the use of prefabricated concrete frame with prefabricated concrete shear walls due to better quality of performance and reduction of manufacturing time is a good option for public multiple floor buildings. These structures in addition to resistance to seismic loads have more flexibility in methods of construction. There is little information about the exact behavior of prefabricated concrete frame with shear walls under earthquake and dynamic loads. Hence much research has been done by various researchers on the seismic behavior of these structures in the form of experimental and analytical models. Today, the main section of the seismic design of buildings is done based on equivalent static force method and calculating earthquake force of design from earthquake linear spectrum by applying a reduction coefficient called behavior coefficient of structure that embrace philosophy of design. So the necessity of determining behavior coefficient with respect to its importance in seismic design of structures seems essential. The behavior coefficient of structure is a coefficient that includes inflexible function of structure and indicates strength and hidden ductility of structure in inflexible stage. In this study various types of pre-fabricated concrete frames together with pre-fabricated 4 and 8-storey shear walls with 1 and 3 bays are studied. The effect of two kinds of uniform and triangular loading on behavior factor has also been taken into consideration. Non-linear static analysis method (Push-over) has been used in order to determine the behavior factor. On the whole, the results have shown that by increasing the bays and building storeys the structural behavior coefficient was increased.

Nonlinear Static Analysis of RC Shear Wall Structure Based on Opensees

To study the seismic performance of RC shear wall, and to develop its fine nonlinear analysis method, systemic studies on nonlinear static analysis and it’s realization method are carried out. Beginning with rotating-angle softened-truss model for coupled shear and flexural responses, analytical model of solid wall is presented based on the comparative study on four types of constitutive law of concrete for confined concrete of boundary zone. Good agreements between analytical and experimental results of load-displacement relation are found, which indicates that the proposed analytical method can reflect the global mechanical behavior of shear wall well. Studies on coupling beam and global perforated wall modeling are implemented, then modeling approach and nonlinear static analysis method for perforated wall are proposed. Comparing analytical load-displacement curve to experimental, initial stiffness and first turning point agree well and analytical ultimate capacity is close to experimental, which is shown that the load-displacement curve can actually exhibit the general load-displacement trend of perforated wall.

Accelerated loosely-coupled CFD/CSD method for nonlinear static aeroelasticity analysis

The flexible high-aspect-ratio wings of high-altitude long-endurance unmanned aerial vehicles experience large geometrical deformations. The nonlinear aeroelastic analysis for such a wing is carried out by using a loosely-coupled CFD/CSD method, which treats the fluid and structure as two separate modules and updates the CFD and CSD variables separately with a transfer of variables at the fluid–structure interface. In the loosely-coupled method employed here, an unsteady Euler solver and a nonlinear CSD solver are joined together by a fully three-dimensional integral constant volume tetrahedron (CVT) interfacing technique. The computation process is very time-consuming when the computed incremental displacements of every aerodynamic node on the wing surface are fully added to the previously computed deformed wing configuration. For a maximum deflection of approximately 8.7 mm (0.54% of semi-span length), the coupled computation scheme takes 20 coupling iteration steps with about 72 hours to converge on an HP XW6400 workstation with a 3 GHz Xeon5160 CPU. To reduce the computational expense of this loosely-coupled method, the golden section technique with an empirical parameter is introduced to speed up convergence. The deflections relaxed by using this technique are assimilated, and the wing bends up monotonically to its static equilibrium position with a maximum deflection 44.9 mm. The convergence history shows that, this accelerated algorithm takes just 6 coupling iteration steps with about 24 hours to monotonically converge to its static equilibrium position, although the maximum deflection 44.9 mm is 5 times larger than the maximum deflection 8.7 mm of the above test case with aeroelastic deflections fully assimilated. So, it is employed in the following nonlinear fluid–structure interaction (FSI) computations. After this nonlinear aeroelastic system has reached its static equilibrium position, the aerodynamic loads on wing surface are extracted and then applied onto the linear wing structure to calculate its deformation. In present paper, if the geometric nonlinear effects are taken into account for wing deflection calculation, the wing structure model is named as “nonlinear wing structure”; otherwise, the wing structure model is named as “linear wing structure”. The role of geometric nonlinearity on aeroelastic deformation is analyzed by comparing the deformations of linear and nonlinear wing structures. It is shown that, geometric nonlinearity plays an important role for large static aeroelastic deformation and should be accounted for in aeroelastic analyses for such high-aspect-ratio flexible wings.

Progressive failure analysis of composite laminated stiffened plates using the finite strip method

A finite strip method for non-linear static analysis based on the tangential stiffness matrix has been developed using the new concept of polynomial finite strip elements, with Mindlin (first-order shear deformable element) plate-bending theory for composite plates. A progressive failure algorithm for composite laminates has been successfully developed for the new finite strip methods using a stress-based failure criterion, Tsai–Wu. A finite strip analysis programming package which is capable of performing non-linear progressive damage analysis for composite stiffened plates and shells has also been developed with Mindlin plate-bending element. Good agreement with the finite element results has been observed through various test cases, confirming the accuracy and reliability of the new developed method.

Evaluation of nonlinear static analysis methods and software tools for seismic analysis of highway bridges

The response of bridges when subjected to seismic excitation can be evaluated by a number of analysis methods. The traditional approach is to employ linear static or dynamic analyses coupled with appropriate modifiers to account for inelastic response while current design practice is moving towards an increased emphasis on nonlinear static analysis methods. In this study, a preliminary seismic response analysis of a two-span highway bridge was performed using linear dynamic analysis procedures to identify the potential for inelastic response. The bridge was subsequently analyzed in accordance with two nonlinear static analysis methods (capacity spectrum and inelastic demand spectrum methods) in an effort to evaluate the difference in global response predicted by the two methods and the effectiveness of various software programs for performing nonlinear static analysis. The results demonstrated that, for the two nonlinear static analysis methods used in this study, different predictions of nonlinear response occurred with neither method being regarded as producing correct results due to a number of simplifications inherent in the methods. Furthermore, the analysis revealed that some software programs are well suited to performing nonlinear static analysis, both from the point-of-view of performing comprehensive analyses and providing a graphical depiction of the evolution of damage (i.e. the behaviour of plastic hinges).

Seismic performance of viaducts with probabilistic method

Due to the uncertainty of both ground motions and structural capacity, it is necessary to consider the seismic performance of viaduct structures using the probabilistic method. The risk is quantified by a procedure on the basis of a numerical determination of the fragility curves. A group of ground motions, Large Magnitude-Short Distance Bin (LMSR-N), selected specially due to its response spectra, is accorded well with the corresponding spectra of the Chinese code for seismic design. The characteristic values of the curvature ductility factors for the serviceability and the damage control limit states are obtained, and two equations for estimating the characteristic values of the curvature ductility factors are developed through regression analysis. Then, the serviceability and damage control limit states were proposed. Three damage states were constituted according the results of the experiment by Pacific Earthquake Engineering Research (PEER) Center. The analytical fragility curves were obtained specifically, using both Capacity Spectrum Method (CSM) (non-linear static) analysis and Ineremental Dynamic Method (IDM) (non-linear dynamic) analysis, respectively, in this paper. The structural fragility curves developed by CSM method can help make the structural analysis simple and quick, avoiding the implementation of the dynamic response history analysis (RHA). Although the dynamic RHA requires a lot of complicated analysis for the structure, the results from RHA are reliable and accurate. Fragility curves are powerful tools for use in performance-based seismic bridge design.

An effective load increment method for multi modal adaptive pushover analysis of buildings

In this study, an effective load increment method for multi modal adaptive non-linear static (pushover) analysis (NSA) for building type structures is presented. In the method, lumped plastisicity approach is adopted and geometrical non-linearties (second-order effects) are included. Non-linear yield conditions of column elements and geometrical non-linearity effects between successive plastic sections are linearized. Thus, load increment needed for formation of plastic sections can be determined directly (without applying iteration or step-by-step techniques) by using linearized yield conditions. After formation of each plastic section, the higher mode effects are considered by utilizing the essentials of traditional response spectrum analysis at linearized regions between plastic sections. Changing dynamic properties due to plastification in the system are used on the calculation of modal lateral loads. Thus, the effects of stiffness changes and local mechanism at the system on lateral load distribution are included. By using the proposed method, solution can be obtained effectively for multi-mode whereby the properties change due to plastifications in the system. In the study, a new procedure for determination of modal lateral loads is also proposed. In order to evaluate the proposed method, a 20 story RC frame building is analyzed and compared with Non-linear Dynamic Analysis (NDA) results and FEMA 356 Non-linear Static Analysis (NSA) procedures using fixed loads distributions (first mode, SRSS and uniform distribution) in terms of different parameters. Second-order effects on response quantities and periods are also investigated. When the NDA results are taken as reference, it is seen that proposed method yield generally better results than all FEMA 356 procedures for all investigated response quantities.

Extension of modal pushover analysis to seismic assessment of bridges

Nonlinear static (pushover) analysis has become a popular tool during the last decade for the seismic assessment of buildings. Nevertheless, its main advantage of lower computational cost compared to nonlinear dynamic time-history analysis (THA) is counter-balanced by its inherent restriction to structures wherein the fundamental mode dominates the response. Extension of the pushover approach to consider higher modes effects has attracted attention, but such work has hitherto focused mainly on buildings, while corresponding work on bridges has been very limited. Hence, the aim of this study is to adapt the modal pushover analysis procedure for the assessment of bridges, and investigate its applicability in the case of an existing, long and curved, bridge, designed according to current seismic codes; this bridge is assessed using three nonlinear static analysis methods, as well as THA. Comparative evaluation of the calculated response of the bridge illustrates the applicability and potential of the modal pushover method for bridges, and quantifies its relative accuracy compared to that obtained through other inelastic methods. Copyright © 2006 John Wiley & Sons, Ltd.

Static analysis of cable networks and their supporting structures

A nonlinear static analysis method for cable structures, particularly emphasizing cable networks, is presented. Cable strains are measured from the current geometry and compressed cables are analytically disassembled with the construction of the equilibrium equation and the stiffness matrix. Finite rotations of cable intersections, referred to as nodes, and cable elements passing through more than two nodes are included in the formulation. An integrated analysis with a linear finite element method is also presented to account for the elastic deformations of supporting structures for the cable networks. The formulation is programmed for a CRAY2 supercomputer using parallel processing to solve the linear equations. Applications of the method used for mesh antenna development are also presented.

Object-oriented non-linear finite element analysis: Application to J2 plasticity

The object-oriented programming concept is applied to the finite element method for non-linear static analysis. Starting from an existing linear object-oriented environment, the question whether the object-oriented approach can be suitably extended to situations where the algorithmic procedure is dominant is examined. The Newton-Raphson and the stress-integration algorithms are presented along with the necessary extensions to the existing objects. The implementation in C+ + is described. The advantage of object-oriented programming is demonstrated, in particular through the concept of non-anticipation of the state of the object.

Cubic B-spline collocation method for nonlinear static analysis of panels under mechanical and thermal loadings

This study presents the cubic B-spline collocation method for solution of one- and two-dimensional nonlinear boundary problems, describing the behavior of panels subjected to mechanical and thermal loadings. Snap-through of panels under pressure loading. and nonlinear thermally-induced response of panels are considered. Available results, yielded by other solution methods, were compared with those obtained by the proposed method. The accuracy, as well as efficiency of the present approach are verified.