Displacement Control Method Research Articles

Geometrically nonlinear quadrature element analysis of spatial curved beams

A novel curved beam quadrature element is presented for geometrically nonlinear analysis of spatial curved beams. Starting from the incremental virtual work equation of the curved beam, the weak form quadrature element method (QEM) is employed to derive the elastic stiffness, geometric stiffness, and induced moment matrices of the curved beam with due account taken of the large rotations in three-dimensional space. All the stiffness matrices are adopted in the incremental-iterative analysis using the generalized displacement control (GDC) method, with specific considerations for the predictor and corrector phases. By testing the constructed curved beam quadrature element with four benchmark problems, it is demonstrated that the element avoids the shear and membrane locking phenomena due to its convenient feature of high-order approximation. In addition, the element is capable of predicting large displacements and rotations, as well as postbuckling paths of spatial beams. Especially, the presented element is featured by unifying the analyses for both curved and straight beams.

A Three-row Opposed Gripping Mechanism with Bioinspired Spiny Toes for Wall-climbing Robots

This paper presents a study of a three-row opposed gripping mechanism made of bioinspired spiny toes. An insect Serica orientalis Motschulsky’s tarsal system was first described and studied. A compliant single spiny toe model was established assuming that the contact asperities were spheres. Following the single toe contact model, a spiny toe array’s contact model was then developed using asperity height’s distribution function. By studying the engaging and disengaging process of the single toe, the mechanical behavior of the toe and toe array were addressed. The toes as well as the arrays were manufactured via rapid prototyping. A customized apparatus using displacement-control method has been carried out to measure the pull-in forces and pull-off positions of the single toe and toe array under various compression conditions. Based on the understanding, a three-row opposed gripping mechanism with radial configuration for wall-climbing robots was designed and fabricated according to the mechanical behaviors of the toe and array. Using an opposed spoke configuration with 3 rows of 31 toes on each linkage array, the mechanism designed as a foot of climbing robots can vertically resist at least 1 kg of load on rough inverted surface, while the maximum normal load is as high as 31 N. The findings may provide a way in developing a high payload wall-climbing robot system for practical applications.

Effect of honeycomb bulkheads on uniaxial undrained bearing capacities of wide-shallow bucket foundation

In order to study the effect of honeycomb bulkheads on uniaxial undrained bearing capacities of wide-shallow bucket foundation, the finite element models of bucket foundations with and without bulkheads on soft ground were established respectively. A large number of 3D finite element analyses have been performed to obtain uniaxial bearing capacities of the two foundations with different embedment ratios and soil shear strength heterogeneity by using displacement control method. The results show that, for homogenous clay, all the vertical, horizontal and moment bearing capacities of the wide-shallow bucket foundation are not affected by the honeycomb bulkheads. For non-homogenous clay, the moment bearing capacity of the wide-shallow bucket foundation is obviously affected by the honeycomb bulkheads, while the effect for improving the vertical and horizontal bearing capacity of the bucket foundation can be neglected. For the convenience of designers reference, simplified calculation equations for undrained bearing capacities are fitted according to the finite element results.

Linear and geometrically nonlinear analysis of plane structures by using a new locking free triangular element

This research is dedicated to propose a high-performance locking-free triangular plane element, which is based on the novel mixed finite element formulation. The new element has six nodes with two transitional degrees of freedom at each node. To improve the displacement and stress responses, a proper mixed interpolation of the strain fields is propounded. Moreover, Mixed Interpolation of Tensorial Components (MITC) has been employed to alleviate in-plane shear locking. The advantage of the employed method is that no additional degrees of freedom are introduced, and spurious instabilities have not been seen. The tensorial forms of the equations are employed in this paper to summarize the formulations. The element passes the numerical tests, which are required to show the accuracy, capability and convergence rate in the structural analysis. Both linear and geometrically nonlinear problems can be solved by the presented formulations. To incorporate the large deformations, Total-Lagrangian formulation will be utilized. Due to completely trace the equilibrium paths of plane problems, especially those with snap-through behavior, a Generalized Displacement Control Method (GDCM) is used as a nonlinear solver. Outcomes of several benchmark problems and some new plane structures, which are analyzed separately, illustrate the high accuracy and advantages of the proposed element, especially in curved structures and nonlinear problems.

Numerical simulation for an estimation of the jacking force of ultra-long-distance pipe jacking with frictional property testing at the rock mass–pipe interface

In ultra-long-distance rock micro-shield pipe jacking, the pipe wall friction resistance is a key factor that determines the magnitude of the jacking force and the layout of the intermediate jacking stations (IJSs), whereas the pipe-rock contact condition is the critical factor controlling the pipe string wall friction resistance. This paper aims to reveal the variation law of the friction resistance between the outer wall of a large-section of concrete pipe string and the surrounding rock during construction via ultra-long-distance rock micro-shield pipe jacking. To that end, the shear friction behaviour and mechanical mechanism was investigated between sandstone and concrete pipe string walls under seven different complex contact conditions (primarily considering various combinations of the three substances, namely, extra-pipe in situ debris, bentonite slurry and sand-laden waste mud at the pipe-rock contact surface) through direct rock shear tests based on the actual pipe-rock contact condition at the Guanjingkou Water Conservancy Project in Chongqing. The average friction coefficient (AFC) of the residual phase of the contact surface under 7 contact conditions was obtained by friction testing. Combined with the contact situation between the surrounding rock and pipe strings at the stage of a rapidly increasing jacking force, a three-dimensional finite element model was established, and the displacement control method was used to simulate the jacking. The comparison with the field monitoring results shows that the numerical model can accurately predict the jacking force and verify the reliability of the AFC parameters in the numerical calculation. Therefore, the combination of indoor testing and the finite element method can be applied to study the jacking force for other ultra-long rock micro-shield pipe jacking applications.

Continuous beam and slab behavior in composite bridge support area without using expansion joint

In a conventional bridge system, there is an expansion joint and a dilatation between superstructure and substructure. If it is not maintained properly, the damage can occur around the expansion joint and on the support. To overcome this problem an alternative type of structure is needed to provide better behavior in the support area. In this study, the type of continuous bridge without an expansion joint is used. Different from continuous bridges in general, in this case, two bearings are used on the pier to facilitate execution. Tests are conducted on two specimens with different types of connection so it is expected to give a significant difference of connection behavior. In the implementation of the test, gravity load is given with a displacement control method. The test results obtained that the ability to receive load of composite beam with steel profile connection has a higher capacity than composite beams with reinforced concrete connection. As for the stiffness value, composite beams with reinforced concrete connection have a higher value than the composite beam load with steel profile connection.

An Efficient Strategy for Solving Structural Nonlinear Equations by Combining the Orthogonal Residual Method and Normal Flow Technique

This paper presents a new procedure for solving structural nonlinear problems by combining the orthogonal residual method (ORM) and normal flow technique (NFT). The perpendicularity condition to the Davidenko flow, introduced by the NFT, which must be satisfied during the iterative process, overcome the difficulties, i.e. the poor convergence and inefficiency of the ORM close to the limit points, particularly the displacement limit points (snap-back behavior). Basically, the idea of the proposed strategy is to adjust the load parameter, which is treated as a variable in the nonlinear incremental-iterative solution process, assuming that the unbalanced forces (residual forces) must be orthogonal to the incremental displacements. This constraint is used together with the NFT perpendicularity condition. The proposed procedure is tested, and its efficiency is corroborated through the analyses of slender shallow and nonshallow arches and an L-frame since they exhibit highly nonlinear behaviors under certain loading conditions. It is concluded that the proposed procedure can overcome the numerical instability problems in the neighborhood of critical points when using only the conventional OR process, and the procedure compares favorably with the arc-length method, minimum residual displacement method, and generalized displacement control method.

Carbon steel and stainless steel bolted connections undergoing unloading and re-loading processes

ABSTRACT A total of 50 bolted connections of carbon steel and stainless steel subjected to monotonic loading and cyclic loading conditions were investigated. The connection specimens were fabricated from carbon steel grades 1.20 mm G500 and 1.90 mm G450, as well as cold-formed stainless steel types EN 1.4301 and EN 1.4162 with nominal thickness 1.50 mm. In the monotonic tests, the specimens were tested under a constant loading rate by the displacement control test method, while in the cyclic tests, the specimens having the same dimensions as those in the monotonic tests were subjected to loading, unloading and re-loading processes, where displacement control and load control test methods were used. The results obtained from the cyclic tests were compared with those obtained from the monotonic tests. It was found that the ultimate loads obtained from the cyclic tests were, on average, larger than those obtained from the monotonic tests for carbon steel bolted connections; this was in contrast with the compared results for stainless steel bolted connections. The elongations corresponding to the ultimate loads obtained from the cyclic tests were, on average, larger than those obtained from the monotonic tests for both carbon steel and stainless steel, which may indicate that the loading processes in the cyclic tests generally delayed the bolted connection specimens from reaching the ultimate loads. Generally, the failure modes in the cyclic tests were consistent with those in the monotonic tests for the same specimen series, where the specimens mainly failed in the connection plate bearing.

Comparative study of algorithms to handle geometric and material nonlinearities

It is critical to handle geometric and material nonlinearities in a stable manner while solving the problems from solid mechanics, such that it results in a converged solution. The present work compares the suitability of generalised displacement control (GDC) and displacement control algorithms (DCA) by solving several 1D and 2D formulations. The ability of these algorithms to handle homogeneous and inhomogeneous deformations is also studied. A novel direct displacement control method (DDCM), coupled with Newton-Raphson method, is proposed and compared with GDC and DCA approaches. Appropriate conclusions are finally drawn based on the successful demonstrations of the numerical results obtained by GDC, DCA and DDCM approaches.

Comparative study of algorithms to handle geometric and material nonlinearities

It is critical to handle geometric and material nonlinearities in a stable manner while solving the problems from solid mechanics, such that it results in a converged solution. The present work compares the suitability of generalised displacement control (GDC) and displacement control algorithms (DCA) by solving several 1D and 2D formulations. The ability of these algorithms to handle homogeneous and inhomogeneous deformations is also studied. A novel direct displacement control method (DDCM), coupled with Newton-Raphson method, is proposed and compared with GDC and DCA approaches. Appropriate conclusions are finally drawn based on the successful demonstrations of the numerical results obtained by GDC, DCA and DDCM approaches.

Hybrid testing with model updating on steel panel damper substructures using a multi‐axial testing system

SummaryThis paper describes a series of hybrid tests performed on a steel panel damper (SPD) specimen by using a multi‐axial testing system. The building under investigation adopted a three‐dimensional six‐story moment resisting frame with four SPDs installed at each story as the main seismic resisting system. The structural model was subjected to bi‐directional ground excitations of three hazard levels. The finite element analysis program “Platform of Inelastic Structural Analysis for 3D Systems” (PISA3D) was used as the analysis kernel for hybrid tests. Relevant programming extensions in PISA3D were created to support geographically distributed hybrid testing in a general‐purpose manner. An external displacement control (EDC) method was developed such that the actual boundary deformation of the specimen fixtures could be continuously measured and immediately compensated during tests. An online model updating (OMU) technique was developed and employed such that the material properties of the specimen could be identified directly from the specimen response during the test. The identified material properties were then immediately used to update those of the other relevant numerical elements to enhance the overall simulation fidelity. Superior flexibility of the underlying software architecture was well demonstrated in this series of hybrid tests since no hardcoding was used to support all the complex test settings. Test results confirmed the effectiveness of the proposed EDC method, as well as the capacity of the proposed OMU technique to satisfactorily and efficiently capture the hysteretic properties of the specimen.

On the Geometrically Nonlinear Analysis of Composite Axisymmetric Shells

Composite axisymmetric shells have numerous applications; many researchers have taken advantage of the general shell element or the semi-analytical formulation to analyze these structures. The present study is devoted to the nonlinear analysis of composite axisymmetric shells by using a 1D three nodded axisymmetric shell element. Both low and higher-order shear deformations are included in the formulation. The displacement field is considered to be nonlinear function of the nodal rotations. This assumption eliminates the restriction of small rotations between two successive increments. Both Total Lagrangian Formulation and Generalized Displacement Control Method are employed for analyzing the shells. Several numerical tests are performed to corroborate the accuracy and efficiency of the suggested approach.

A new improved fiber plastic hinge method accounting for lateral-torsional buckling of 3D steel frames

This paper presents a new advanced analysis method, specifically a new improved fiber plastic hinge method, for analyzing the nonlinear inelastic behavior of 3D steel frames accounting for lateral-torsional buckling. The second-order effects are considered by the use of the geometric stiffness matrix and stability functions obtained from the exact solution of beam-columns under axial force and bending moments at two ends. The spread of plasticity along the member length due to both residual stresses and the impact of axial force is considered by utilizing the Column Research Council (CRC) tangent modulus concept, while the gradual yielding due to flexure is represented by two fiber plastic hinges at the ends of the element. The lateral-torsional buckling stiffness matrix is established by the virtual work principle using the updated Lagrangian formulation. The generalized displacement control method is applied to solve the nonlinear equilibrium equations in an incremental-iterative scheme. The nonlinear load-displacement behavior and ultimate load results compare well with those of previous studies. It is concluded that accurately using only one element per member likely predicts the second-order inelastic behavior of 3D steel frames including the effect of lateral-torsional buckling.

Geometrically nonlinear analysis of FG doubly-curved and hyperbolical shells via laminated by new element

An isoparametric six-node triangular element is utilized for geometrically nonlinear analysis of functionally graded (FG) shells. To overcome the shear and membrane locking, the element is improved by using strain interpolation functions. The Total Lagrangian formulation is employed to include the large displacements and rotations. Finding the nonlinear behavior of FG shells via laminated modeling is also the goal. A power function is employed to formulate the variation of elastic modulus through the thickness of shells. The results are presented in two ways, including the general FGM formulation and the laminated modeling. The equilibrium path is obtained by using the Generalized Displacement Control Method. Some popular benchmarks, including hyperbolical shell structures are solved to declare the correctness and accuracy of proposed formulations.

Sensitivity Analysis for Displacement-Controlled Finite-Element Analyses

Displacement-controlled finite-element analyses are typically employed to simulate the nonlinear static response of structural systems where a loss of load carrying capacity due to localized material failure and/or geometric nonlinearity is expected. To utilize applications such as reliability, optimization, and system identification for structural systems where the peak load capacity is a random variable or where the performance function is defined in terms of the applied load, accurate and efficient gradients of the displacement-controlled response are required. The direct differentiation method (DDM) is applied to the displacement control method in order to compute response sensitivity with respect to the applied load, which is treated as a variable within each pseudotime step. The resulting sensitivity gives the change in structural load carrying capacity with respect to changes in uncertain parameters. To verify the derived sensitivity equations, comparisons between the DDM and the finite-difference method (FDM) are performed through standalone sensitivity analyses of structural systems with material and geometric nonlinearity. Reliability analyses of a steel frame show the importance measures obtained when the performance function is defined in terms of the structural resistance to applied loads in a displacement-controlled analysis are similar to those obtained in a load-controlled analysis where the performance function is defined in terms of the structural displacements.

Thermal Post-buckling Analysis of Moderately Thick Nanobeams

As a first attempt, the thermal buckling and post-buckling behaviors of moderately thick nanobeams subject to uniform temperature rise are investigated via employing the differential quadrature method (DQM). Considering the von-Karman’s assumptions, governing equations of the nanobeams are derived using the Eringen’s nonlocal elasticity theory in conjunction with the first-order shear deformation beam theory. The differential quadrature method is used to discretize the governing equations. The direct iterative displacement control method is coupled with the DQM to solve the nonlinear system of algebraic equations. Rapid rate of convergence and accuracy of the method for solving the problem are shown, and effects of the small-scale parameters on the thermal buckling and post-buckling behaviors of the nanobeams for different boundary conditions and length-to-thickness ratios are demonstrated.

Strong-Form Formulated Generalized Displacement Control Method for Large Deformation Analysis

The traditional analysis of geometric nonlinearity is mostly based on the weak-formulated Galerkin method such as the finite element method. The element nature has limited its application as a result of numerical integration in the governing equation and quality control of deformed mesh. In the middle of 1990s, the meshfree methods have been developed and become one leading research topic in computational mechanics. Especially, the strong form collocation methods require no additional efforts to process numerical integration and impose Dirichlet boundary condition, thereby making the collocation methods computationally efficient. In the incremental–iterative process, how to accurately reflect the change in the slope of the load–deflection curve of the structure and remain numerically stable are of major concerns. Thus, we propose a strong-form formulated generalized displacement control method to analyze geometric nonlinear problems, where the radial basis collocation method is adopted. The numerical examples demonstrate the ability of the proposed method for large deformation analysis.

A weak-form quadrature element formulation for 3D beam elements used in nonlinear and postbuckling analysis of space frames

Abstract A weak-form quadrature element formulation is presented for the three-dimensional beam element for use in the geometrically nonlinear and postbuckling analysis of space frames. Starting from the virtual work equation of a beam in the linearized, incremental sense, the quadrature element method (QEM) is employed to derive the elastic stiffness, geometric stiffness, and induced moment matrices of the beam with due account taken of the large rotations in three-dimensional space. All the stiffness matrices are adopted in the incremental-iterative analysis using the generalized displacement control (GDC) method, with specific considerations for the predictor and corrector phases. By comparing the results obtained for all the benchmark problems studied with existing ones, it is demonstrated that the present formulation is capable of predicting large displacements and rotations, as well as the postbuckling paths of space frames. The present formulation is featured by the fact that it is simple, straightforward, and reliable.

Vulnerability Assessment Of Marine Structures: A Case Study On Jetty

Jetties are one of the most important structures in the coastal area, which can be used for transporting large quantities of goods and raw materials from one place to the other. Their functionality is very much essential because they are lifeline structures of the country. It is observed during the past earthquakes that jetties have been damaged even under mild shaking. Damaged and unserviceable jetties cause delay of export and import business. It directly affects the economy of particular region in terms of business, employment and growth. This clearly indicates the need to design these facilities so that they can withstand natural disasters particularly earthquakes and tsunamis. In this paper, a study has been carried out to find out the damage (D) to the Jetty. The Jetty is modeled using 2D Applied Element Method (AEM) to perform damage analysis of structure. Pushover analysis is done to get base shear vs roof displacement of building using displacement control method. Using the dissipated energy approach, damage is quantified at every displacement level and normalized to 1. A fragility curve has been developed to quantify the damage of Jetty with respect to different peak ground accelerations. The damage values were calculated for the PGA values of KHF Mandvi, NKF Jodiya and KMF Jhangi and found that the Jetty got light damage (D=0.2), and moderate damage (D=0.38 and 0.42) respectively.

Force Method for Displacement Adjustment of Prestressed Cable Structures with Dynamic Relaxation Method

The stiffness of prestressed cable structure is provided by self-stress, and the self-stress of the structure is sensitive to external errors due to their high flexibility. Based on the basic theory of the force method (FM) and stochastic search technique, the linear displacement control problem was converted to an optimization question. Genetic algorithm (GA) is used to solve this optimization problem for prestressed structures of linear behavior. And then the dynamic relaxation method (DRM) is introduced to the linear displacement control method to achieve the non-linear displacement control for prestressed structures of non-linear behavior. The non-linear displacement control consists of two phases: (1) use the linear displacement control method as the controller step to determine the selection of actuation members and the variation of these selected members, and (2) use the DRM as the corrector step to calculate the equilibrium state of structures after linear controller deformation. A numerical example is conducted which shows that the non-linear control and the linear control both are in well agreement with the target values in the case of small displacement adjustment, while in the case of large displacement adjustment, the former is superior to the latter.