Aims. We have used FLAMES (the Fibre Large Array Multi Element Spectrograph) at the VLT-UT2 telescope to obtain spectra of a large sample of red giant stars from the inner disk of the LMC, ∼2 kpc from the center of the galaxy. We investigate the chemical abundances of key elements to understand the star formation and evolution of the LMC disk: heavy and light [s-process/Fe] and [α/Fe] give constraints on the time scales of formation of the stellar population. Cu, Na, Sc, and the iron-peak elements are also studied aiming to better understand the build up of the elements of this population and the origin of these elements. We aim to provide a more complete picture of the LMC's evolution by compiling a large sample of field star abundances. Methods. LTE abundances were derived using line spectrum synthesis or equivalent width analysis. We used OSMARCS model atmospheres and an updated line list. The [heavy-s/light-s] ratios are high, showing a slow, increasing trend with metallicity. We were surprised to find an offset for three of the iron-peak elements. We found an offset for the [iron-peak/Fe] ratios of Ni, Cr, and Co, with an underabundant pattern and subsolar values, while Vanadium ratios track the solar value. Copper shows very low abundances in our sample for all metallicities, compatible with those of the Galaxy only for the most metal-poor stars. The overall chemical distributions of this LMC sample indicates a slower star formation history relative to that of the solar neighborhood, with a higher contribution from type Ia supernovae relative to type II supernovae.