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The general structure of geometrically‐based automatic finite element modelling systems is discussed. The development of a specific system employing the modified‐quadtree and modified‐octree mesh generators is presented. The application of this approach to metal forming analysis is then given.

This paper aims to discuss selected components of finite element (FE) implementation of the modelling approach proposed in Part 1 of this paper. To put forward a simple and efficient method of enhancing shear stress transverse distribution. To demonstrate model performance.

Developed elements employ polynomial interpolation with hierarchic/bubble modes and use assumed strain method to suppress numerical locking.

Using well‐established concepts of FE technology is shown to provide a simple and robust tool for geometric non‐linear analysis of laminated beams. Presented numerical results highlight the need of including shear deformations in geometric non‐linear analysis of laminated structures with large transverse anisotropy.

The proposed model is dedicated to geometric non‐linear FE analysis of laminated beams undergoing large planar displacements, subject to small strains and moderate interlayer slips.

A versatile FE is provided for geometric nonlinear analysis of laminated structures with large transverse anisotropy.

Apart from the geometries to be dealt with, rapid prototyping (RP) of heterogeneous objects requires additional material information to be processed. This generally involves a large amount of information to be processed simultaneously. The robustness and efficiency problems, which seem less critical in homogeneous solid fabrications, become an issue. The direct impetus of this paper is to present robust and efficient algorithms for RP of heterogeneous objects.

The robustness is benefited from using the proposed non‐manifold heterogeneous cellular model, which guarantees gap‐free material depositions around material interfaces. The efficiency enhancement is achieved by eliminating repetitive boundary intersections and using a heuristic material interrogation approach.

By using the proposed algorithms, the robustness and efficiency of RP of heterogeneous objects can be improved. It is found that an average 30 percent efficiency improvement is obtained using the proposed heuristic material interrogation approach.

Non‐manifold heterogeneous cell representation (HC‐Rep) is used in RP fields for the first time. Based on the HC‐Rep, the robustness and efficiency of RP of heterogeneous object is addressed in this paper.

In the vibration reduction field, constrained stand-off layer damping cylindrical shell plays an important role. However, due to the lack of accurate analysis of its damping characteristics, this hinders its further research and application. Therefore, the purpose of this paper is concerned with an accurate solution for the vibration-damping characteristics of a constrained stand-off-layer damping cylindrical shell (CSDCS) under various classical boundary conditions and conducts a further analysis.

Based on the Rayleigh–Ritz method and the Hamilton principle, a dynamic model of CSDCS is established. Then the loss factor and the frequency of CSDCS are obtained. The correctness and convergence behavior of the present model are verified by comparing the calculation results with the literature. By using for various classical boundary conditions without any special modifications in the solution procedure, the characteristics of CSDCS with S-S, C-C, C-S, C-F and S-F boundaries are discussed.

The Rayleigh–Ritz method is effective in handling the problem of CSDCS with different boundaries and an accurate solution is obtained. The boundary conditions have an important influence on the vibration and damping behavior of the CSDCS.

Based on the Rayleigh–Ritz method and Hamilton principle, a dynamic model of CSDCS is established for the first time, and then the loss factor and frequency of CSDCS are obtained. In addition, the effectiveness of adding the stand-off layer between the base shell and the viscoelastic layer is confirmed by discussing the characteristics of CSDCS with S-S, C-C, C-S, C-F and S-F boundaries.

The purpose of this paper is to present an algorithm for determining the inner and outer loops of arbitrary parametric surfaces.

The algorithm considers two sub-algorithms: one for non-closed surfaces and another one for closed surfaces. The first sub-algorithm named by area positive and negative method (APNM), combines a curve discretization algorithm with the polygon direction judgment algorithm to judge the inner and outer loops of non-closed surfaces. The second sub-algorithm, called by cross-period number method (CPNM), combines a curve discretization algorithm with the periodicity of closed surfaces to judge the type of boundary loops.

The APNM can use less CPU time to determining the inner and outer loops of the non-closed parametric surfaces. The CPNM can also determine the inner and outer loops of closed parametric surfaces effectively. The judgment results of loops can ensure that the direction of meshes generated on these surfaces is right. And finally ensure the correctness of the numerical simulation results.

Several numerical examples presented have verified the robustness and efficiency of the proposed algorithm. Compared with the conventional algorithm, the more complex the model, the more time the APNM saves in the process of determining the inner and outer loops for non-closed surfaces. The CPNM is also a new method to determining the inner and outer loops for closed parametric surfaces. The single run-time of CPNM is very small and can reach the level of microseconds.

The purpose of the present paper is to describe the modeling, analysis and simulations for the resin transfer molding (RTM), manufacturing process with particular emphasis on the sensitivity analysis for non‐isothermal applications.

For the manufacturing of advanced composites via RTM, besides the tracking of the resin flow fronts through a porous fiber perform, the heat transfer and the resin cure kinetics play an important role. The computational modeling is coupled multi‐disciplinary problem of flow‐thermal‐cure. The paper describes the so‐called continuous sensitivity formulation via the finite element method for this multi‐disciplinary problem for process modeling of composites manufactured by RTM to predict, analyze and optimize the manufacturing process.

Illustrative numerical examples are presented for two sample problems which include examination of sensitivity parameters for the case of material and geometric properties, and boundary conditions including fill time sensitivity analysis. The results indicate that the proposed formulations serve a useful role for the design and optimization of the RTM manufacturing process, thereby, avoiding heuristic trial‐and‐error methods.

The paper restricts attention to constant properties and extensions to non‐linear thermophysical properties will serve as an added benefit.

The present efforts significantly impact the design/optimization process in the process modeling of composites manufactured by RTM.

To the authors' knowledge, this is the first time that continuous sensitivity analysis is done for non‐isothermal considerations in RTM.

Advanced Placement Human Geography continues to grow in popularity at the secondary level, but not without its supporters and critics. The purpose of this paper is to examine one critique, the lack of critical geography and then give two examples how teachers could incorporate it using inquiry.

Critical geography examines the praxis between space, place and identity, exposing power imbalances constructed within space and place. Critical geographers also consider how to transform space and place to be more equitable. This paper provides two examples of how critical geography can be infused into content covered in AP Human Geography using the C3 Framework and the Inquiry Design Model. By infusing critical geographic perspectives into AP Human Geography students practice asking questions about inequities in space and place with an opportunity to become agents of transformation.

There is a gap in AP Human Geography when it comes to incorporating critical geography. This paper looks to redress that by providing two examples on how critical geography could be used in an AP Human Geography curriculum.

This collection of two inquiries is given as ways that AP Human Geography instructors could incorporate critical geography into their classrooms.

The purpose of this work is to apply the Fourier–Ritz method to study the vibration behavior of the moderately thick functionally graded (FG) parabolic and circular panels and shells of revolution with general boundary conditions.

The modified Fourier series is chosen as the basis function of the admissible functions of the structure to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges, and the vibration behavior is solved by means of the Ritz method. The complete shells of revolution can be achieved by using the coupling spring technique to imitate the kinematic compatibility and physical compatibility conditions of FG parabolic and circular panels at the common meridian of θ = 0 and 2π. The convergence and accuracy of the present method are verified by other contributors.

Some new results of FG panels and shells with elastic restraints, as well as different geometric and material parameters, are presented and the effects of the elastic restraint parameters, power-law exponent, circumference angle and power-law distributions on the free vibration characteristic of the panels are also presented, which can be served as benchmark data for the designers and engineers to avoid the unpleasant, inefficient and structurally damaging resonant.

The paper could provide the reference for the research about the moderately thick FG parabolic and circular panels and shells of revolution with general boundary conditions. In addition, the change of the boundary conditions can be easily achieved by just varying the stiffness of the boundary restraining springs along all the edges of panels without making any changes in the solution procedure.

Introducing the concept of a design domain to truss topology optimization, this paper presents an algorithm generating geometrically admissible ground structures on possibly concave (or even disconnected) 3D design domains. That is a set of connections between nodal points actually respecting the geometry of the design domain. Since ground structures may be applied in other contexts the presentation does not assume any specifics of truss topology optimization. However, in the example section an application of ground structures in a truss topology optimization problem may be found.

The penalty boundary method (PBM) is a new method for performing finite element analysis using a regular overlapping mesh that does not have to coincide with the geometric boundaries. The PBM uses CAD solid geometry directly to generate element matrix equations and apply boundary conditions, removing the need for a separate representation of the geometry. The preliminary results show that the PBM can significantly reduce the time and manual intervention required to prepare finite element models and perform analyses. This paper presents the PBM approach for representing the problem domain on an overlapping mesh that results in a more traditional method for applying natural boundary conditions.