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Based on mechanics principles and solved numerically on a super workstation, Ford has developed various sheet metal forming analysis computer programs. This paper describes the features in these programs. Several actual design examples illustrate how stamping engineers use these tools to evaluate and improve their design.

In this paper, we introduce a numerically stable 2D computer model for sheet metal forming analysis based on the membrane theory. It simulates both axisymmetrical and plane strain cases with various restraining and friction conditions. We implemented a more realistic material model that accounts for cyclic loading and unloading. Also, the difficult frictional force reversal problem has been overcome. A simulation package released within Ford Motor Company has proven robust and accurate for applications to industrial cases.

This paper describes the capability of the binder analysis in Ford's three dimensional sheet metal forming program. Three real design examples illustrate that the program could detect buckling/wrinkling in auto-body panels during binder set (wrap). With revision of the binder surface design, the program predicted buckling/wrinkling on those panels disappeared. The computing time for each evaluation of the binder set of a panel is in order of minutes on a super workstation; therefore, it has been used as a design analysis tool.

An existing binder computer program including a pre-processor to establish a finite element model has been modified so that it can analyze the blank of a trunk deck-lid outer panel with pre-bend. The formula for computing the spring-back shape after a blank under cylindrical bending with a specific radius is derived in this paper. Using this spring-back shape as a starting configuration instead of a flat blank, the modified program computes the binder wrap of an automotive body panel. Two trunk deck-lid outer panels were analyzed to illustrate the effects of pre-bend.

A finite element program based on the nonlinear shell theory, membrane plus bending, and the flow theory of plasticity has been developed to analyze stresses and deformation during the three stages of the stretch-draw forming process. A surface contact problem with friction is formulated in this paper and solved by means of the developed program. It is applied to two actual body outer-panels in this paper to demonstrate the capability and features of the program. Computing time for an overall analysis of these three forming stages of the stretch-draw forming process is reasonable. Therefore, it is practical to use this program for evaluation of design of the forming process.

An earlier report(1) described an approximate optimization technique which was applied to the design of a Fairmont/Zephyr decklid, predicting a potential weight reduction of about 20% compared to the production decklid. The validity of the design technique has been evaluated by fabricating prototype decklids to the optimized design and measuring the appropriate properties, The prototype decklids consisting of 0.024in.(0.61mm) gage inner and outer panels with a redesigned inner panel configuration were essentially equivalent to the design objective production decklid in bending and torsion. In addition, the prototypes passed the engineering specification tests for oil canning and dent resistance. A weight saving of approximately 5-6lbs(2.3-2.7kgs) (15-18%) was achieved relative to the production decklid.

An analytical procedure has been developed to evaluate the relative damageability of a bumper with respect to the geometrical and material properties by means of a nonlinear thin shell computer program as reported at the last VSM conference. The analysis has been extended to determine the effects of various high strength steels with different prestrains on bumper damageability since the fabrication procedure will induce varying degrees of prestrain in the finished bumper. The effect of prestrain is particularly important for dual phase steels because of the lower initial yield to tensile strength ratio of these materials. The analysis was carried out for three types of steels of potential use for bumpers, namely SAE 950X, SAE 980X and DP 980. The relative damageability of bumpers in these steels was evaluated analytically for various levels of prestrains.

A simplified bumper model was established for evaluation of relative damageability with respect to the geometrical and material properties of an automobile bumper. Applying a nonlinear shell computer program developed at Ford Research Staff, we have studied the section of a prototype bumper and three idealized bumper sections. The computer results were used to describe the relative damage to four bumper sections. A drop weight test was conducted on the prototype bumper model and the test results were found to be in good agreement with the anlytical predictions.

This is a subsequent report on a study of the sheet metal response subjected to impact loads. The mathematical model of thin shells employed in the previous report is used once again to model the sheet metal. Based upon nonlinear shell theory, the flow theory of plasticity, and the finite element technique, the equilibrium conditions in the incremental form at each nodal point are established. Step-by-step numerical integration is applied to solve these equations and an error control procedure is incorporated at every load level. A computer program has been written according to this formulation and development. It was checked by running two sample problems for which solutions exist in the literature and one problem whose solution was experimentally evaluated from a full size structure. In addition applications relative to finding the dent resistance and oil-canning deformations of sheet metal body components in an automotive structure are discussed.