Kinematic Formulation Research Articles

Possibilities and limitations of the sequential kinematic method for simulating evolutionary plasticity problems

Evolutionary plasticity processes, such as ploughing and penetrating, widely exist in many geotechnical engineering applications. The simulation of these processes poses considerable challenges due to the occurrence of large deformation, unsteady nature of the material free surface, and inherent coupling between mechanical response and material geometries. This paper explores the possibility of simulating the first-order response of these processes by using sequential kinematic method (SKM) in combination with simple deformation mechanism. The mechanism consists of rigid elements separated by velocity discontinuities. Computations based on the kinematic approach of limit analysis are sequentially performed to evaluate the most likely deformation mode and update material geometries. An r-adaptive kinematic formulation is used that captures versatile velocity fields by optimizing the geometries of simple kinematic mechanism. The modelling methodology is studied in detail for two archetypal evolutionary plasticity problems: wedge ploughing Tresca material and cylinder penetrating undrained clay. The numerical results obtained by using the SKM are compared against existing analytical and numerical solutions, as well as experimental evidence. The paper demonstrates that evolutionary plasticity problems can be simulated in a conceptually simple way using SKM and highlights the potential pitfalls of this technique.

Efficient kinematic upper-bound limit analysis for hole/inclusion problems by adaptive XIGA with locally refined NURBS

Limit analysis can be used to directly calculate the ultimate load of structures without considering cumbersome elastic–plastic analysis. We present an adaptive mesh refinement strategy by mean of extended isogeometric analysis (XIGA) in association with second-order cone programming (SOCP) for kinematic limit analysis of hole and inclusion problems. The location of hole and inclusion can be captured by level set function without regard for its interfaces. The local refined non-uniform rational B-splines (LR NURBS), allowing local refinement and modeling complex geometries, are selected as basis functions. The structured mesh refinement strategy is exploited to carry out local refinement on the basis of the indicator of L2-norm of plastic strain rates. The adaptive local refinement can detect the local plastic deformation regions, and further reveals the possible failure mechanisms. The discrete kinematic formulation of limit analysis can be rewritten as the form of SOCP, and further is solved efficiently with the help of the Mosek toolbox. All the desirable features of the present approach are illustrated through numerical experiments.

Dynamic modeling, system identification and comparative study of various control strategies for a spatial parallel manipulator

The significant challenges seen with the mathematical modeling and control of spatial parallel manipulators are its difficulty in the kinematic formulation and the inability to real-time control. The analytical approaches for the determination of the kinematic solutions are computationally expensive. This is due to the passive joints, solvability issues with non-linear equations, and inherent kinematic constraints within the manipulator architecture. Therefore, this article concentrates on an artificial neural network–based system identification approach to resolve the complexities of mathematical formulations. Moreover, the low computation time with neural networks adds up to its advantage of real-time control. Besides, this article compares the performance of a constant gain proportional–integral–derivative (PID), variable gain proportional–integral–derivative, model predictive controller, and a cascade controller with combined variable proportional–integral–derivative and model predictive controller for real-time tracking of the end-effector. The control strategies are simulated on the Simulink model of a 6-degree-of-freedom 3-PPSS (P—prismatic; S—spherical) parallel manipulator. The simulation and real-time experiments performed on the fabricated manipulator prototype indicate that the proposed cascade controller with position and velocity compensation is an appropriate method for accurate tracking along the desired path. Also, training the network using the experimentally generated data set incorporates the mechanical joint approximations and link deformities present in the fabricated model into the predicted results. In addition, this article showcases the application of Euler–Lagrangian formalism on the 3-PPSS parallel manipulator for its dynamic model incorporating the system constraints. The Lagrangian multipliers include the influence of the constraint forces acting on the manipulator platform. For completeness, the analytical model results have been verified using ADAMS for a pre-defined end-effector trajectory.

Robust control of a cable-driven rehabilitation robot for lower and upper limbs

In this research, a redundant cable-driven robust rehabilitation robot has been proposed for helping and automating the proper function of the patient’s lower and upper limbs in the presence of uncertainties, disturbances, noise, and time delay using a new control algorithm to derive the best tracking with the least deviations. A new joint limit avoidance path-planning method is exerted while maintaining the bounds of upper and lower angles. Also, a new robust motion controller, namely computed-torque-like controller with a variable-structure compensator was applied to the system and compared with computed-torque controller outputs. Thus, showing the efficiency of the mentioned control algorithm in the presence of uncertainties, disturbances, noise, and time delay and its superior performance and robustness in spatial motions are the goals of this paper as well as taking advantage of a new path-planning approach.Firstly, the kinematic formulation of the cables is obtained. Then, a joint limit avoidance theory is used to apply upper and lower bounds for the joint angles. In the next step, Lagrangian dynamic equations for the 3D motions are derived. Subsequently, the positive and unilateral tension conditions in cable-driven systems are applied using null-space solutions. To have precise tracking and robustness with the existence of uncertainties, disturbances, noise, and time delay, a computed-torque control and robust computed-torque-like controller with a variable-structure compensator are utilized for the system. Stability analyses of the controllers are presented and the obtained results are compared for tracking a spatial reference trajectory.Ultimately, this controller witnessed an improvement in the lower limb with the existence of uncertainties and disturbances in terms of the robustness of the given method about 19.5 percent, and in cable forces about 17.1 percent. Improvements for the tracking errors and the control inputs were 10.8 and 7.3 percent in the presence of noise, and 7.3 and 8.6 percent in the presence of the time delay respectively. Similar results were obtained for the upper limb with 21 percent improvement in control inputs and 21.1 percent improvement in tracking performance respectively.

Computational efficiency of multi-body systems dynamic models

AbstractFor several decades, simulation and analysis of mechanisms have been performed with dedicated computer-aided engineering software that implements general dynamic formulations, known in the literature as multi-body systems (MBS) formulations. The MBS name is related to the structure of the mechanism, which is often considered to be a collection of bodies interconnected by mechanical joints (pairs). Nevertheless, only a few formulations are really based on a true multi-body mechanical model, while many others instantiate mathematically quite different mechanical concepts. This paper aims to identify and discuss the mechanical models that fundament the main multi-body mathematical formulations known in the literature. The main features of each model are outlined, based on a detailed presentation of the structure and equations of motion, together with their link with the kinematic and dynamic formulations. A comparative study related to computational efficiency is then presented for the identified main models, based on a test mechanism. Comparative advantages and disadvantages are discussed at the end, considering the identified mechanical models.

Modeling and Analysis of a Glass Façade Robot

For glass façade cleaning, we developed a reconfigurable robot, Mantis-mini, with a dry cleaning mechanism and linear actuator based transitioning mechanism. It consists of three suction modules, connected by a support structure and each suction module has individual differential drive wheels with independent steering capability. This paper focuses on the detailed design of the platform, static structural analysis for and kinematic formulation. The adhesion performance of the suction module is evaluated using experiments, Computational Fluid Dynamics (CFD) simulations, and analytically formulated estimation. The suction pressure magnitude predicted from the simulations increases with suction impeller speed and agrees well with measurements and analytical calculation in terms of order of magnitude and qualitative trend. An adaptive proportional-integral (PI) controller is designed and implemented for regulating suction pressure and motion controller of the platform. The suction performance of the platform is validated through real-time experiments of the platform on the glass surface.

Vibration response of a geometrically discontinuous bi-directional functionally graded plate resting on elastic foundations in thermal environment with initial imperfections

The present study includes the free vibration analysis of geometrically imperfect and discontinuous porous functionally graded bi-directional plate (B-FGP) resting on an elastic foundation in a thermal environment. The geometric discontinuity is present in the form of a circular cutout at the center of the plate whereas initial imperfections have been incorporated in terms of geometric as well as porosity inclusions. The kinematic formulation is based on the refined non-polynomial trigonometric higher-order shear deformation theory (HSDT). A new porosity model has been developed to incorporate the influence of the microstructure defect on the effective material properties of the B-FGP. The gradation of properties is done along the thickness (z-direction) as well as the length (x-direction) of the plate using the power-law distribution. A new expression has been given to obtain the solution of the non-linear temperature rise along the thickness of the B-FGP. A continuous Lagrangian four-noded quadrilateral element has been used to perform the finite element formulation with eight degrees of freedom per node. The equations of motion have been derived using a variational approach. The validation and comparative study have been done to authenticate the present formulation. The influence of the cutout radius, elastic foundation parameters, porosity, thermal environment, geometric imperfection, and volume fraction indexes has been discussed in detail.

Optimal Factorization of the State-Dependent Riccati Equation Technique in a Satellite Attitude and Orbit Control System

The satellite attitude and orbit control system (AOCS) can be designed with success by linear control theory if the satellite has slow angular motions and small attitude maneuver. However, for large and fast maneuvers, the linearized models are not able to represent all the perturbations due to the effects of the nonlinear terms present in the dynamics and in the actuators (e.g., saturation). Therefore, in such cases, it is expected that nonlinear control techniques yield better performance than the linear control techniques. One candidate technique for the design of AOCS control law under a large maneuver is the State-Dependent Riccati Equation (SDRE). SDRE entails factorization (that is, parameterization) of the nonlinear dynamics into the state vector and the product of a matrix-valued function that depends on the state itself. In doing so, SDRE brings the nonlinear system to a (nonunique) linear structure having state-dependent coefficient (SDC) matrices and then it minimizes a nonlinear performance index having a quadratic-like structure. The nonuniqueness of the SDC matrices creates extra degrees of freedom, which can be used to enhance controller performance, however, it poses challenges since not all SDC matrices fulfill the SDRE requirements. Moreover, regarding the satellite's kinematics, there is a plethora of options, e.g., Euler angles, Gibbs vector, modified Rodrigues parameters (MRPs), quaternions, etc. Once again, some kinematics formulation of the AOCS do not fulfill the SDRE requirements. In this paper, we evaluate the factorization options (SDC matrices) for the AOCS exploring the requirements of the SDRE technique. Considering a Brazilian National Institute for Space Research (INPE) typical mission, in which the AOCS must stabilize a satellite in three-axis, the application of the SDRE technique equipped with the optimal SDC matrices can yield gains in the missions. The initial results show that MRPs for kinematics provides an optimal SDC matrix.

Fractional-order structural stability: Formulation and application to the critical load of nonlocal slender structures

This study presents a framework to perform stability analysis of nonlocal solids whose behavior is described according to the fractional-order continuum theory. In this formulation, space fractional-order operators are used to capture the nonlocal response of the medium by means of nonlocal kinematic relations. We use the geometrically nonlinear fractional-order kinematic relations within an energy based approach to establish the Lagrange-Dirichlet stability criteria for nonlocal structures. This energy based approach to nonlocal structural stability is possible due to a positive-definite and thermodynamically consistent definition of the deformation energy enabled by the fractional-order kinematic formulation. The Rayleigh-Ritz coefficient for critical load is also derived for linear buckling conditions. The fractional-order formulation is finally used to determine critical loads for buckling of the slender nonlocal beams and plates using a dedicated fractional-order finite element solver. Results establish that, in contrast to existing studies, the effect of nonlocal interactions is observed on both the material and the geometric stiffness, when using the fractional-order kinematics approach. These observations are supported quantitatively via the solution of case studies that focus on the critical buckling response of fractional-order nonlocal slender structures, and a direct comparison of the fractional-order approach with classical nonlocal approaches.

A Versatile Inverse Kinematics Formulation for Retargeting Motions Onto Robots With Kinematic Loops

Robots with kinematic loops are known to have superior mechanical performance. However, due to these loops, their modeling and control is challenging, and prevents a more widespread use. In this letter, we describe a versatile Inverse Kinematics (IK) formulation for the retargeting of expressive motions onto mechanical systems with loops. We support the precise control of the position and orientation of several end-effectors, and the Center of Mass (CoM) of slowly walking robots. Our formulation safeguards against a disassembly when IK targets are moved outside the workspace of the robot, and we introduce a regularizer that smoothly circumvents kinematic singularities where velocities go to infinity. With several validation examples and three physical robots, we demonstrate the versatility and efficacy of our IK on overactuated systems with loops, and for the retargeting of an expressive motion onto a bipedal robot.

Kinestatic Analysis of General Parallel Manipulators

Robotic mechanisms in general can be of either serial-chain, parallel-chain, or hybrid (a combination of both parallel and serial chains) geometry. While it can be asserted that kinematic theories and techniques are well established for fully serial-chain manipulators, the same assertion cannot be made when it is considered in the general context. In this article, we present a general procedure for systematic formulation and characterization of the instantaneous kinematics for a robotic mechanism with a general parallel-chain geometry. A kinestatic approach based on screw system theory is adopted in this treatment. The resulting equation is a compact Jacobian matrix of the system which includes attributes from not only the active joints but also the passive constraints. An example has been provided to demonstrate the methodology as well as its theoretical feasibility.

Continuous adjoint complement to the Blasius equation

This manuscript is concerned with a continuous adjoint complement to two-dimensional, incompressible, first-order boundary-layer equations for a flat plate boundary layer. The text is structured into three parts. The first part demonstrates that the adjoint complement can be derived in two ways, following either a first simplify then derive or a first derive and then simplify strategy. The simplification step comprises the classical boundary-layer (BL) approximation, and the derivation step transfers the primal flow equation into a companion adjoint equation. The second part of the paper comprises the analyses of the coupled primal/adjoint BL framework. This leads to similarity parameters, which turn the partial-differential-equation (PDE) problem into a boundary value problem described by a set of ordinary-differential-equations (ODEs) and support the formulation of an adjoint complement to the classical Blasius equation. Opposite to the primal Blasius equation, its adjoint complement consists of two ODEs, which can be simplified depending on the treatment of advection. It is shown that the advective fluxes, which are frequently debated in the literature, vanish for the investigated self-similar BL flows. Differences between the primal and the adjoint Blasius framework are discussed against numerical solutions, and analytical expressions are derived for the adjoint BL thickness, wall shear stress, and subordinated skin friction and drag coefficients. The analysis also provides an analytical expression for the shape sensitivity to shear driven drag objectives. The third part assesses the predictive agreement between the different Blasius solutions and numerical results for Navier–Stokes simulations of a flat plate BL at Reynolds numbers between 103≤ReL≤105. It is seen that the reversal of the inlet and outlet locations and the direction of the flow, inherent to the adjoint formulation of convective kinematics, poses a challenge when investigating real finite length (finite Re-number) flat plate boundary layer problems. Efforts to bypass related issues are discussed.

Post-Yield characteristics of electrorheological fluids in nonlinear vibration analysis of smart sandwich panels

The present study deals with the nonlinear free vibration analysis of sandwich plates containing electrorheological (ER) fluid as the core layer. Since yield stress of the ER fluid is relatively low, the fluid widely operates in the post-yield region in which the shear stress and shear strain relation is no longer linear. This study employs an equivalent linearized complex shear modulus to quantify the storage and loss moduli of the fluid in different levels of shear strain amplitude and electric field intensity. Also, Classical Plate Theory (CPT) along with von Kármán kinematic formulations are incorporated to extract governing equations of motion of the ER based sandwich plates, in a finite element formulation. The nonlinear governing equations of motion of the structure are solved using a displacement control strategy to evaluate the resonant frequencies and corresponding loss factors of the sandwich plate. Then, the primary attention is focused on the effect of post-yield characteristics of ER fluid on the nonlinear dynamic behavior of the ER based sandwich structure. Furthermore, the effect of applied electric field, boundary conditions and plate parameters such as core layer thickness on the natural frequencies and damping of the structure are comprehensively investigated.

An Uncertainty-Driven and Observability-Based State Estimator for Nonholonomic Robots

The problem addressed in this article is the localization of a mobile robot using a combination of onboard sensors and ultrawideband (UWB) beacons. By using a discrete-time formulation of the system's kinematics, we identify the geometric conditions that make the system globally observable and cast the state estimation problem into the framework of least-squares optimization. The observability filter thus obtained is remarkably different from classic Bayesian filters, such as the Kalman Filter, since it does not need a priori stochastic models of process and measurement uncertainty contributions and thus proves to have better performance than the Kalman filters if such contributions are partly unknown or differ from the expected values. The second important outcome of this work is the analytical study of uncertainty propagation. The effectiveness of the designed filter, the validity of the theoretical analysis of estimation uncertainties, and the comparisons with a state-of-the-art extended Kalman filter (EKF) are corroborated by extensive simulations and validated experimentally.

Curved p-version C1 finite elements for the finite deformation analysis of isotropic and composite laminated thin shells in irregular shape

In this work, we generalize our recently developed p-version curved C1 plate elements to the finite deformation analysis of general isotropic and laminated thin shells with arbitrary curvature and shape. The kinematic formulations are based on the geometrically-exact nonlinear thin shell model where the Kirchhoff-Love hypothesis is strictly implemented during the deformation. Since high accurate curved coarse meshes are required in the implementation of p-version finite element method, the quasi regional mapping technique is employed and modified to obtain the high-order meshes with fitted boundaries. Through this method, shells with irregular shapes can be easily modeled. To avoid dealing the difficult problem of constructing fully C1 conforming displacement fields on shell surface, the C1 conformity of present elements is implemented on the selected Gauss-Lobatto nodes, which had been found to be able to produce very fast convergence. Nodal variables including second-order directional derivatives on surfaces are derived and used for element assembly. In this manner, direct construction of displacement fields on shell mid-surface defined by the quasi regional mapping is allowed. Several benchmark problems of large deformation analysis of isotropic and laminated thin shells are presented to illustrate the accuracy as well as robustness of the present method.

Accuracy Analysis of Machining Trajectory Contemplating Workpiece Dislocation on a Six Degree of Freedom Machining Bed

Machining is material removal from a workpiece. Current spindle technologies allow the material to be removed very quickly but unfortunately this compromises the accuracy of the desired machined trajectory on the workpiece. Proposed solution to the problem is restricting motion of the tool and giving rotation to the workpiece. This paper presents analysis of the accuracy of trajectory of material removal from a workpiece, such that the workpiece rotates with six degrees of freedom, in the presence of error generated due to an offset of the workpiece from centre of the moving platform of the machining bed. The kinematics of the machining bed is, therefore, modeled using as inverse kinematic formulation applying geometric and vector addition method. The mechanism outputs three rotational and three translational motions. The leg length for each of six legs of the bed is computed individually. Moreover, workpiece position offset error is modelled to find actual leg lengths of the bed. Finally accuracy computation model is proposed to analyse the accuracy of the final trajectory of the motion of the workpiece. The models are verified in simulation for a trajectory and validated experimentally on a six degree of freedom (6DOF) machining bed. The results reveal maximum inaccuracy in machining trajectory to be 1% in experiments while less than 1% in simulation. This verifies quality of the mechanism and efficacy of the proposed 6DOF machining bed in machining accuracy.

A Thermodynamically Consistent Formulation for Dynamic Response of Thermoviscoelastic Plate/Shell Based on Classical Continuum Mechanics (CCM)

This paper presents a thermodynamically consistent and kinematic assumption free formulation for dynamics of thermoviscoelastic plates/shells based on the conservation and balance laws of classical continuum mechanics (CCM) in which dissipation mechanism has been incorporated through ordered rate constitutive theory for deviatoric stress tensor. In this paper, we consider small deformation, small strain. The conservation and balance laws of CCM in [Formula: see text] in Lagrangian description using Cauchy stress tensor ([Formula: see text]) and linearized Green strain tensor ([Formula: see text]) constitute the mathematical model. The constitutive theory for the deviatoric Cauchy stress ([Formula: see text]) is derived using conjugate pairs in entropy inequality in conjunction with representation theorem. The argument tensors of [Formula: see text] are [Formula: see text] and rates of [Formula: see text] up to order [Formula: see text]. This yields a constitutive theory with dissipation mechanism based on rates of strain up to order [Formula: see text]. Constitutive theory for heat vector is also derived using the conjugate pairs in the entropy inequality and representation theorem. Finite element method is used to obtain solutions of the initial value problems descried by the balance of linear momenta (BLM), energy equation and the constitutive theories. The shell element geometry is described by the middle surface and the nodal vectors at the middle surface defining bottom and top surfaces of the element. The local approximation for the displacement field is [Formula: see text] - version hierarchical in the plane of the element as well as in the transverse direction. A space-time decoupled finite element formulation using Galerkin Method with Weak Form (GM/WF) in space is constructed for BLM as well as energy equation, both resulting in ordinary differential equations (ODEs) in time. The ordinary differential equations (ODEs) in time resulting from the finite element formulation of BLM are used to study: (i) natural undamped modes of vibration (ii) the transient dynamic response using the ODEs in time recast in modal basis: (a) using Rayleigh damping (b) using the ordered rate damping proposed in this paper. Time response is calculated using modal damping based on Rayleigh damping as well as using the proposed ordered rate damping mechanism. Model problem studies are presented to demonstrate: (1) accuracy of the natural frequencies obtained from the present formulation for thin and thick plates/shells (in which shear deformation is significant) and the results are compared with the currently used plate formulations (2) accuracy of damped transient response using proposed damping mechanism is compared with time response using Rayleigh damping (3) it is shown that Rayleigh damping has no physical basis and leads to spurious stationary states. The proposed damping yields accurate stationary states that are in exact agreement with the solution of corresponding BVP. A single formulation presented in this paper remains valid and accurate for very thin as well as very thick plates/shells and correctly simulates 3D state of deformation regardless of plate/shell thickness and is free of shear locking problems as well as need for shear corrections. When obtaining the time response, solution for an increment of time alternates between the solution of BLM followed by the solution of the energy equation. Details are presented in the paper.

Thermodynamically consistent thermoelastic plate and shell formulations for small deformation and small strain using non-classical continuum mechanics incorporating internal rotations

The work presented in a recent paper by the authors [35] for a thermodynamically consistent and kinematic assumption free plate and shell formulation for small deformation and small strain based on the conservation and balance laws of classical continuum mechanics (CCM) is extended here for non-classical continuum mechanics (NCCM). This formulation incorporates additional physics due to internal rotations that arise due to the deformation gradient tensor. This physics is neglected in CCM, hence is absent in the plate and shell formulation of reference [35]. Consideration of this new physics requires modifications of the current balance laws as well as consideration of a new balance law “balance of moment of moments” (BMM) [2, 3]. Cauchy stress tensor becomes non-symmetric. Cauchy moment tensor is conjugate to the symmetric part of the rotation gradient tensor which exists now due to new physics. Balance of angular momenta yields additional three differential equations as part of the mathematical model. The new balance law (BMM) establishes symmetry of the Cauchy moment tensor. The new physics considered here exists in all deforming solid continua as it is due to the deformation gradient tensor, but is ignored in CCM. The consequence of this new physics is additional stiffness, hence additional strain energy storage and change in the time history of displacements and stress field compared to formulations based on CCM. The basic mathematical model for the plate and shell deformation consists of conservation and balance laws in $$\mathbb {R}^3$$ based on NCCM incorporating internal rotations. The associated finite element formulations for obtaining the solution of the mathematical model consists of : (i) geometry of the plate or shell described by the flat or curved middle surface (as done conventionally) and nodal vectors locating the top and bottom faces of the plate/shell (ii) the displacement field approximation that is p-version hierarchical in the plane as well as in the transverse direction (iii) integral form is constructed using Galerkin Method with Weak Form (GM/WF) and the corresponding element equations. The formulation presented here remains valid and accurate for thin as well as thick plate/shell and naturally reduces to the formulation of reference [35] based on classical continuum mechanics. Model problem studies and comparisons with the studies based on CCM formulation [35] will be presented in a follow up paper.

PhysCap

Marker-less 3D human motion capture from a single colour camera has seen significant progress. However, it is a very challenging and severely ill-posed problem. In consequence, even the most accurate state-of-the-art approaches have significant limitations. Purely kinematic formulations on the basis of individual joints or skeletons, and the frequent frame-wise reconstruction in state-of-the-art methods greatly limit 3D accuracy and temporal stability compared to multi-view or marker-based motion capture. Further, captured 3D poses are often physically incorrect and biomechanically implausible, or exhibit implausible environment interactions (floor penetration, foot skating, unnatural body leaning and strong shifting in depth), which is problematic for any use case in computer graphics. We, therefore, present PhysCap , the first algorithm for physically plausible, real-time and marker-less human 3D motion capture with a single colour camera at 25 fps. Our algorithm first captures 3D human poses purely kinematically. To this end, a CNN infers 2D and 3D joint positions, and subsequently, an inverse kinematics step finds space-time coherent joint angles and global 3D pose. Next, these kinematic reconstructions are used as constraints in a real-time physics-based pose optimiser that accounts for environment constraints ( e.g. , collision handling and floor placement), gravity, and biophysical plausibility of human postures. Our approach employs a combination of ground reaction force and residual force for plausible root control, and uses a trained neural network to detect foot contact events in images. Our method captures physically plausible and temporally stable global 3D human motion, without physically implausible postures, floor penetrations or foot skating, from video in real time and in general scenes. PhysCap achieves state-of-the-art accuracy on established pose benchmarks, and we propose new metrics to demonstrate the improved physical plausibility and temporal stability.

A six-node prismatic solid finite element for geometric nonlinear problems in elasticity

The present work deals with an extended six-node prismatic 3D solid finite element to the analysis of nonlinear geometrical problems. The kinematic formulation is based on a virtual Space Fiber Rotation (SFR) concept which conducts to improve the displacement fields with additional displacement terms, presenting rotational degrees of freedom (DOFs). Once the standard and patch tests for linear validation are previously achieved, the present element is assessed again for large displacement and moderate rotation. For this purpose, the total Lagrangian approach is used and the Green–Lagrange strain/Piola–Kirchhoff​ stress tensors are considered. The material behavior considered in this work is restricted to Saint-Venant–Kirchhoff model for 3D large displacements elasticity To demonstrate the efficiency and accuracy of the developed finite element model, extensive and standard nonlinear benchmarks are presented. The obtained results show a good convergence and accuracy compared to similar finite elements and consequently well capability of the present element to deal with geometric nonlinear problems, including prediction of several limit points.