In this article, the propagation of one-dimensional stress waves in a plate made of functionally graded materials excited by a harmonic force is studied. The material properties of the functionally graded material plate are assumed to be graded in the thickness direction according to a power law distribution in terms of the volume fractions of the constituents. The governing equations are based on stress–strain relation and the equation of motion. Keeping generality, the functionally graded material plate is assumed as a multilayer with linear material property in each layer while arbitrary exponential material property through the thickness. A plate made of aluminum and alumina is considered as an example to illustrate the effects of the volume fraction exponent and number of layers on the wave propagation characteristics. Results indicate that by changing the exponent values (M), stress distribution can be controlled. Also at every certain power law (M), there exist a number of layers beyond which no variation in stress can be detected on the plate response. Furthermore, the wave in time domain is also investigated and the effects of material distribution on the wave speed are examined.

Frontal vehicle structure is of high importance through crash energy managements and crash boxes are the fundamental structural component for vehicle safety as well as after sales issues. Similar to many other vehicle components, the detail design of crash box is usually part of manufacture knowhow. However, some guide lines are always available. In this article a general procedure is introduced for designing of crash box with the aid of novel thin walled structures and according to conventional crash scenarios. The problem is followed through some basic steps. Firstly, the crash box idea is selected through a wide range of previous investigated elements and is packaged in a real bench vehicle. Then thanks to the protection provided by the new crash box on the other more expensive components (e.g. headlamp, cooling pack, etc.), the effectiveness of this element are acknowledged through the low speed offset crash. Further on the robustness of new proposed crash box is approved by high speed crash simulations. The quasi-static simulations implemented during the analyses are carried out by finite element explicit code (Abaqus) and the FE modeling and dynamic simulation through the next steps are also performed in ANSA and PAM CRASH respectively. Finally in addition to the general crash box design proposed procedure, the achieved results demonstrated that the corrugated conical thin walled tubes deforms in regular and rather stable shape under both axial and oblique loadings. They also produced a reasonable reaction force versus deformations which leads to stiff and crashworthy energy absorber in comparison to traditional rectangular and even some special models like as origami shapes, and so they could be a valuable selection for crash box implementations in passenger cars.

Deformation modeling of an infinite plate of functionally graded materials (FGMs) loaded by normal force to the plate surface is studied. The material properties of FGM plate are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The governing equations are based on stress-strain relation and the equilibrium force equation. Keeping generality, FGM plate has been assumed as a multilayer with linear material property in each layer while arbitrary exponential material property through the thickness. A plate made of Aluminum and Alumina is considered as an example to illustrate the effects of the volume fraction exponent and number of layers on the plate deformation response. Effects of number of layers on the accuracy of the plate behavior under external load are examined. Results indicate that at every certain power-law (M), there exist a number of layers beyond which no variation can be detected on the plate deformation response.

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