Bias Truck Tire Deformation Analysis with Finite Element Modeling

This paper presents a method for modeling of pneumatic bias tire axisymmetric deformation. A previously developed model of all-steel radial tire was expanded to include the non-linear stress–strain relationship for textile cord and its thermal shrinkage. Variable cord density and cord angle in the cord-rubber bias tire composite are the major challenges in pneumatic tire modeling. The variabilities result from the tire formation process, and they were taken into account in the model. Mechanical properties of the composite were described using a technique of orthotropic reinforcement overlaying onto isotropic rubber elements, treated as a hyperelastic incompressible material. Due to large displacements, the non-linear problem was solved using total Lagrangian formulation. The model uses MSC.Marc code with implemented user subroutines, allowing for the description of the tire specific properties. The efficiency of the model was verified in the simulation of mounting and inflation of an actual bias truck tire. The shrinkage negligence effect on cord forces and on displacements was examined. A method of investigating the influence of variation of cord angle in green body plies on tire apparent lateral stiffness was proposed. The created model is stabile, ensuring convergent solutions even with large deformations. Inflated tire sizes predicted by the model are consistent with the actual tire sizes. The distinguishing feature of the developed model from other ones is the exact determination of the cord angles in a vulcanized tire and the possibility of simulation with the tire mounting on the rim and with cord thermal shrinkage taken into account. The model may be an effective tool in bias tire design.

Isogeometric Optimal Design of Compliant Mechanisms Using Finite Deformation Curved Beam Built-Up Structures

This paper presents a configuration and sizing design optimization method for large deformation planar compliant mechanisms, using a continuum-based adjoint design sensitivity analysis (DSA) approach for built-up structures. Under the total Lagrangian formulation, the Jaumann strain formulation using the discretization of the global displacement field is employed to account for the finite deformation of arbitrarily curved Kirchhoff beams. In multipatch models, a rotational junction continuity condition is imposed using penalty and Lagrange multiplier methods. The developed adjoint DSA method can handle nonconservative loading conditions, which lead to asymmetry of tangent operator. Performance measures are displacements and rotation angles, and neutral axis configuration and cross-sectional thickness are considered as design variables. Also, analytical design sensitivity expressions for the rotation continuity condition are derived. Various compliant mechanisms including path-generators and an angular rotator are synthesized to demonstrate the applicability of the proposed method.

FSI analysis and simulation of flexible blades in a Wells turbine for wave energy conversion

In this paper a preliminary design and a 2D computational fluidstructure interaction (FSI) simulation of a flexible blade for a Wells turbine is presented, by means of stabilized finite elements and a strongly coupled approaches for the multi-physics analysis. The main objective is to observe the behaviour of the flexible blades, and to evaluate the eventual occurrence of aeroelastic effects and unstable feedbacks in the coupled dynamics. A series of configurations for the same blade geometry, each one characterized by a different material and mechanical properties distribution will be compared. Results will be given in terms of total pressure difference, supported by a flow survey. The analysis is performed using an in-house build software, featured of parallel scalability and structured to easy implement coupled multiphysical systems. The adopted models for the FSI simulation are the Residual Based Variational MultiScale method for the Navier-Stokes equations, the Total Lagrangian formulation for the nonlinear elasticity problem, and the Solid Extension Mesh Moving technique for the moving mesh algorithm.

An Optimized Approach for Tracing Pre- and Post-Buckling Equilibrium Paths of Space Trusses

In this paper, a novel optimization-based method is proposed to analyze steel space truss structures undergoing large deformations. The geometric nonlinearity is considered using the total Lagrangian formulation. The nonlinear solution is obtained by introducing and minimizing an objective function subjected to the displacement-type constraints. The proposed approach can fully follow the equilibrium path of the geometrically nonlinear space truss structures not only before the limit point, but also after it, namely, including both the pre- and post-buckling paths. Moreover, a direct estimation of the buckling loads and their corresponding displacements is possible by using the method. Particularly, it has been shown that the equilibrium path of a structure with highly nonlinear behavior, multiple limit points, snap-through, and snap-back phenomena can be traced via the proposed algorithm. To demonstrate the accuracy, validity, and robustness of the proposed procedure, four benchmark truss examples are analyzed and the results compared with those by the modified arc-length method and those reported in the literature.

Total Lagrangian Formulation for Large Deformation Modeling Using Uniform Background Mesh

Mesh generation difficulties can be avoided when a background mesh rather than a mesh that conforms to the geometry is used for the analysis. The geometry is represented by equations and is independent of the mesh and is immersed in the background mesh. The solution to boundary value problems is approximated or piece-wise interpolated using the background mesh. The main challenge is in applying the boundary conditions because the boundaries may not have any nodes on them. Implicit boundary method has been used for linear static and dynamic analysis and has shown to be an effective approach for imposing boundary conditions but has never been applied to nonlinear problems. In this paper, this approach is extended to large deformation nonlinear analysis using the Total Lagrangian formulation. The equations are solved using the widely used modified Newton-Raphson method with loads applied over many load steps. Several test examples are studied and compared with traditional finite element analysis software for verification.