Abstract: First FEA mesh model representing 3-D geometry of a carbon fiber reinforced composite (CFRC) product/part, pre-forming fiber orientation and desired reference fiber direction at a particular location on the product/part are received. First FEA mesh model contains finite elements associated with respective material properties for carbon fibers and binding matrix. Pre-forming fiber orientation includes number of fibers and relative angles amongst the fibers. Pre-forming 2-D shape of a workpiece used for manufacturing the product/part is obtained by conducting a one-step inverse numerical simulation that numerically expands the first to a second FEA mesh model based on numerically-calculated structural behaviors according to respective material properties. Pre-forming fiber orientation is superimposed on the second FEA mesh model with the desired reference fiber direction being preserved.

Abstract: A 3-D mesh model represents 3-D geometry of a product/part manufactured with deep draw metal forming process. The 3-D model contains nodes connected by shell finite elements. 3-D model is modified by converting each quadrilateral shell finite element to triangular shell finite elements. Respective averaged nodal curvatures of all nodes of the 3-D model is calculated based on the 3-D geometry. A 2-D mesh model is created by unfolding the 3-D model to a plane while maintaining all corresponding triangular shell finite elements between the 2-D and the 3-D models as similar triangles. An estimated pre-stamped shape of a workpiece used for manufacturing the product/part is obtained by iteratively updating the 2-D model with a set of internal nodal forces with respect to the 3-D model and with a set of nodal force adjustments based on the respective averaged nodal curvatures.

Abstract: First FEA mesh model representing 3-D geometry of a carbon fiber reinforced composite (CFRC) product/part, pre-forming fiber orientation and desired reference fiber direction at a particular location on the product/part are received. First FEA mesh model contains finite elements associated with respective material properties for carbon fibers and binding matrix. Pre-forming fiber orientation includes number of fibers and relative angles amongst the fibers. Pre-forming 2-D shape of a workpiece used for manufacturing the product/part is obtained by conducting a one-step inverse numerical simulation that numerically expands the first to a second FEA mesh model based on numerically-calculated structural behaviors according to respective material properties. Pre-forming fiber orientation is superimposed on the second FEA mesh model with the desired reference fiber direction being preserved.

Abstract: A 3-D mesh model represents 3-D geometry of a product/part manufactured with deep draw metal forming process. The 3-D model contains nodes connected by shell finite elements. 3-D model is modified by converting quadrilateral shell finite element to triangular shell finite elements, if there are at least one quadrilateral shell finite element in the 3-D model. Respective averaged nodal curvatures of all nodes of the 3-D model is calculated based on the 3-D geometry. A 2-D mesh model is created by unfolding the 3-D model to a plane while maintaining all corresponding triangular shell finite elements between the 2-D and the 3-D models as similar triangles. An estimated pre-stamped shape of a workpiece used for manufacturing the product/part is obtained by iteratively updating the 2-D model with a set of internal nodal forces with respect to the 3-D model and with a set of nodal force adjustments based on the respective averaged nodal curvatures.

Abstract: First FEA mesh model representing 3-D geometry of a carbon fiber reinforced composite (CFRC) product/part, pre-forming fiber orientation and desired reference fiber direction at a particular location on the product/part are received. First FEA mesh model contains finite elements associated with respective material properties for carbon fibers and binding matrix. Pre-forming fiber orientation includes number of fibers and relative angles amongst the fibers. Pre-forming 2-D shape of a workpiece used for manufacturing the product/part is obtained by conducting a one-step inverse numerical simulation that numerically expands the first to a second FEA mesh model based on numerically-calculated structural behaviors according to respective material properties. Pre-forming fiber orientation is superimposed on the second FEA mesh model with the desired reference fiber direction being preserved.

Abstract: First FEA mesh model representing 3-D geometry of a carbon fiber reinforced composite (CFRC) product/part, pre-forming fiber orientation and desired reference fiber direction at a particular location on the product/part are received. First FEA mesh model contains finite elements associated with respective material properties for carbon fibers and binding matrix. Pre-forming fiber orientation includes number of fibers and relative angles amongst the fibers. Pre-forming 2-D shape of a workpiece used for manufacturing the product/part is obtained by conducting a one-step inverse numerical simulation that numerically expands the first to a second FEA mesh model based on numerically-calculated structural behaviors according to respective material properties. Pre-forming fiber orientation is superimposed on the second FEA mesh model with the desired reference fiber direction being preserved.

Abstract: Numerically-simulated physical behaviors of workpiece sheet metal during a metal forming process having a predefined load path is obtained based on received FEA mesh model and mesh adjustment criteria as follows: initializing current simulation time; determining current simulation period from current simulation time and next mesh adjustment time; using characteristic length to establish a 3-D mesh refinement zone that contains a space encompassing a corresponding section of the predefined load path for the current simulation period; updating the FEA mesh model by refining those finite elements located within the 3-D mesh refinement zone to a desired level and by coarsening certain finite elements outside of the zone according to mesh coarsening criterion; conducting corresponding portion of the time-marching simulation using the updated FEA mesh model for current simulation period until current simulation time reaches next mesh adjustment time; and repeating until current simulation time passes the total simu

Abstract: First FEA mesh model representing 3-D geometry of a carbon fiber reinforced composite (CFRC) product/part, pre-forming fiber orientation and desired reference fiber direction at a particular location on the product/part are received. First FEA mesh model contains finite elements associated with respective material properties for carbon fibers and binding matrix. Pre-forming fiber orientation includes number of fibers and relative angles amongst the fibers. Pre-forming 2-D shape of a workpiece used for manufacturing the product/part is obtained by conducting a one-step inverse numerical simulation that numerically expands the first to a second FEA mesh model based on numerically-calculated structural behaviors according to respective material properties. Pre-forming fiber orientation is superimposed on the second FEA mesh model with the desired reference fiber direction being preserved.

Abstract: First FEA mesh model representing 3-D geometry of a carbon fiber reinforced composite (CFRC) product/part, pre-forming fiber orientation and desired reference fiber direction at a particular location on the product/part are received. First FEA mesh model contains finite elements associated with respective material properties for carbon fibers and binding matrix. Pre-forming fiber orientation includes number of fibers and relative angles amongst the fibers. Pre-forming 2-D shape of a workpiece used for manufacturing the product/part is obtained by conducting a one-step inverse numerical simulation that numerically expands the first to a second FEA mesh model based on numerically-calculated structural behaviors according to respective material properties. Pre-forming fiber orientation is superimposed on the second FEA mesh model with the desired reference fiber direction being preserved.

Abstract: Numerically-simulated physical behaviors of workpiece sheet metal during a metal forming process having a predefined load path is obtained based on received FEA mesh model and mesh adjustment criteria as follows: initializing current simulation time; determining current simulation period from current simulation time and next mesh adjustment time; using characteristic length to establish a 3-D mesh refinement zone that contains a space encompassing a corresponding section of the predefined load path for the current simulation period; updating the FEA mesh model by refining those finite elements located within the 3-D mesh refinement zone to a desired level and by coarsening certain finite elements outside of the zone according to mesh coarsening criterion; conducting corresponding portion of the time-marching simulation using the updated FEA mesh model for current simulation period until current simulation time reaches next mesh adjustment time; and repeating until current simulation time passes the total simu