Solid Mechanics Analysis Research Articles

Experimental and theoretical studies of shrinkage, warpage, and sink marks of crystalline polymer injection molded parts

AbstractAn integrated theory and computer program were developed in this study for simulation of shrinkage, warpage, and sink marks of crystalline polymer injection molded parts. The basic theory considers the following items: (1) mold cooling analysis; (2) analysis of the polymeric filling, packing, and cooling processes; (3) viscoelastic behavior of polymeric fluid; (4) influence of thermal and mechanical properties of polymer; (5) pressure‐volume‐temperature relationship of polymer; (6) crystallization kinetics of crystalline polymer; and (7) solid mechanics analysis. Considered are the origins of defects, e.g. nonuniform cooling process, nonuniform volume shrinkage, flow‐induced residual stress, thermal induced residual stress, and crystallization behavior. The boundary element and the finite difference method were applied toward calculating the mold cooling analysis for obtaining the temperature profile at the cavity surface as the boundary conditions in filling and packing analysis. A hybrid finite‐element and finite‐difference methods were employed for simulating the injection molding filling, packing, and cooling processes. A control volume method was applied towards both finding the melt front position and also calculating the temperature and pressure profile at any instant during the filling process. A modified Tait equation provided a description of the pressure‐volume‐temperature relationship of crystalline polymers. The Malkin's kinetics model was employed to describe the behavior of polymer crystallization. The flow‐induced and thermal induced‐residual stresses employed as the initial conditions in the solid mechanics analysis were obtained with the linear thermo‐viscoelastic model. The displacements, including the thickness direction of part, which could not be calculated by the traditional bending moment method, were solved by using the numerical solid mechanics analysis with the three dimensional finite element method. These methods were applied to predict the shrinkage, warpage, and sink marks of crystalline polypropylene and amorphous ABS for the plate cavity. Both the qualitative results for the theoretical prediction correlated sufficiently with the experimental data. The theoretical results were also correlated using the commercial software C‐MOLD.

The displacement-type finite element approach—From art to science

The finite element method originated in the aerospace industry in the mid- 1950s to solve practical stress analysis problems associated with the struc- tural design of aerospace vehicles. It is today the most overwhelmingly popular analysis and design tool in structural and solid mechanics and is being extensively applied to a very wide spectrum of engineering science, e.g. fluid mechanics, heat transfer and electromagnetics. In its formative years, the development of the method was guided mostly by engineering intuition, heuristic judgment and trial and error experimentation and vali- dation. Its achievements have been remarkable and there are now very power- ful general-purpose software codes that make a variety of analyses and design tasks routinely simple, that were once considered to be intractable. This is not to say that the progress of the method has been free of hurdles, especi- ally in finding a complete scientific basis for it. Based on the recent stud -ies of this author and his colleagues, this review attempts to provide a more complete paradigmatic understanding of the issues involved. Concepts such as consistency and ( variational) correctness are introduced. These together with the more familiar completeness and continuity requirements are then employed to guide the construction of error-free robust finite elements and also provide procedures to perform a priori error estimates for the quality of approximation. These C-concepts, as we shall call them, are elucidated and their relevance to the design of several key elements commonly found in general-purpose packages used by the aerospace, automobile and mechanical engineering industries is briefly covered. The article reviews what has been achieved in areas where the C-concepts can be applied fruitfully in the study of the displacement type finite element method.

Sensitivity analysis and shape optimization in nonlinear solid mechanics

The objective of this paper is twofold. First, it presents a boundary element formulation for sensitivity analysis for solid mechanics problems involving both material and geometric nonlinearities. The second focus is on the use of such sensitivities to obtain optimal design for problems of this class. Numerical examples include sensitivity analysis for small (material nonlinearities only) and large deformation problems. These numerical results are in good agreement with direct integration results. Further, by using these sensitivities, a shape optimization problem has been solved for a plate with a cutout involving only material nonlinearities. The difference between the optimal shapes of solids, undergoing purely elastic or elasto-viscoplastic deformation is shown clearly in this example.

Design sensitivity analysis of non‐linear structural systems part I: Theory

AbstractA unified approach is presented for design sensitivity analysis of non‐linear structural systems that include truss, beam, plane elastic solid and plate components. Both geometric and material non‐linearities are treated. Sizing design variables, such as thickness and cross‐sectional areas of components of individual members and built‐up structures, are considered. A distributed parameter structural design sensitivity analysis approach is used that retains the continuum elasticity formulation throughout the derivation of design sensitivity analysis results. Using this approach and an adjoint variable method, expressions for design sensitivity in terms of design variations are derived in the continuous setting which can be evaluated numerically using analysis results of finite element analysis. Both total Lagrangian and updated Lagrangian formulations in non‐linear analysis of solid mechanics are used for design sensitivity analysis. Numerical implementation of design sensitivity analysis results using existing finite element code will be presented in Part II of this paper.

Dynamic analysis in solid mechanics by an alternative boundary element procedure : Brebbia, C A; Nardini, D Soil Dynam Earthq EngngV2, N4, Oct 1983, P228–233

Dynamic analysis in solid mechanics by an alternative boundary element procedure : Brebbia, C A; Nardini, D Soil Dynam Earthq EngngV2, N4, Oct 1983, P228–233

A mixed eulerian-lagrangian displacement model for large-deformation analysis in solid mechanics

A new mixed kinematic description for large-deformation solid mechanics is presented. The novel aspect of the new model is that both the initial and current configurations are treated as unknown. Large-deformation statements of the principles of virtual work and stationary potential energy are formulated with the new description and presented in incremental form suitable for iterative finite element solutions. The well-known total Lagrangian and updated Lagrangian descriptions are shown to be special cases of the mixed formulation. The new description is advantageous in situations where it is difficult to select an appropriate material discretization prior to analysis. Applications to large-deformation frictional contact and fracture mechanics are presented to demonstrate the utility of the new kinematic description.

Dynamic analysis in solid mechanics by an alternative boundary element procedure

A new procedure for eigenvalue and transient dynamic analyses in solid mechanics is presented here using a boundary integral approach. Contrary to previous work, it is shown in this paper that by applying a special class of co-ordinate functions one can obtain the mass matrix using boundary values. As a consequence, the free vibration case is reduced to an algebraic eigenva problem, while transient vibrations can be solved by using a direct time integration procedure.

Some consideration on the finite element method

AbstractIn order to break the present deadlock of finite element non‐linear analysis in solid mechanics, the importance of consideration of slip phenomena in inelastic problems is pointed out and a series of new simplified elements are introduced which may be powerful in the discrete analysis of highly non‐linear problems.

A Discrete Method of Analysis on Fluid Dynamics Problem (1 st Report)

Recently the finite element method for analysis of flow problems has been established and a number of important contributions are being reported every year all over the world.It is common practice to use the higher order shape functions for these finite element flow analysis. Use of the higher order shape functions, however, may present a serious problem on computing time and cost in practice and it is believed that this situation will be more critical in case of flow analysis than in case of nonlinear analysis of solid mechanics problems.In view of such a situation, use of the lower order shape functions will be proposed in the finite element analysis of flow problems in this paper. In this approach, the higher derivative of velocity components, for example, will be approximated by the finite difference expression of the lower order derivatives. Therefore, it is expected that computing time for matrix manipulation will be considerably reduced. So far, application of this method has been made to analysis of KdV equation in the shallow water wave, steady creep flow and the potential flow problems. Results of these analysis have duly proved validity of this method. In this paper application will be attempted to analysis of the Navier-Stokes equation and discussion will be presented in comparison with existing finite element method.