of bellows 200 can be designed with a feature to define a mounting hinge support 225 as shown in one such case the thickness of these discs can be different than the others on the bellows of selected convolutions also this convolution can be located at any point along the bellows the exact mounting configuration is dependent upon the application another aspect of this invention includes consideration of and a solution to the interconnection of the elements and structures described above with relatively thicker wall connection pipes or components thereof found in for example an exhaust system more specifically it will be appreciated that the foregoing flexible elements and bellows apparatus described above have particular applicability to or use in exhaust systems for internal combustion engines wherein the pipes or conduits of such systems not shown or their connecting structures are relatively thicker than the members comprising the bellows components or stamping described above in these and other cases there is here consideration of how the flexible bellows invention described above are operably interconnected within such systems or to specific connection pipes or other exhaust components to this end the invention further contemplates the combination to the bellows described above of end caps configured for welding or other attachment to the ends of the bellows and more particularly to the end bellows component disc or stamping the end caps are somewhat thicker than the bellows discs to facilitate welding both to the bellows and to much thicker conduits or pipe components of an exhaust system this aspect of the invention is illustrated in fig5 8 where fig5 illustrates in perspective the addition of end caps 250 251 to a bellows 252 such as that illustrated previously in fig1 g for example but wherein the.